当前期刊: Experimental Mathematics Go to current issue    加入关注   
显示样式:        排序: IF: - GO 导出
我的关注
我的收藏
您暂时未登录!
登录
  • An Algorithm for Determining Torsion Growth of Elliptic Curves
    Exp. Math. (IF 0.659) Pub Date : 2020-07-13
    Enrique González–Jiménez; Filip Najman

    We present a fast algorithm that takes as input an elliptic curve defined over Q and an integer d and returns all the number fields K of degree d ′ dividing d such that E ( K ) tors contains E ( F ) tors as a proper subgroup, for all F ⊈ K . We ran this algorithm on all elliptic curves of conductor less than 400.000 (a total of 2.483.649 curves) and all d ≤ 23 and collected various interesting data

    更新日期:2020-07-14
  • Where Do the Maximum Absolute q-Series Coefficients of (1 − q)(1 − q2)(1 − q3)…(1 − qn − 1)(1 − qn) Occur?
    Exp. Math. (IF 0.659) Pub Date : 2020-07-06
    Alexander Berkovich; Ali Kemal Uncu

    Abstract We used the MACH2 supercomputer to study coefficients in the q-series expansion of (1−q)(1−q2)…(1−qn), for all n≤75000. As a result, we were able to conjecture some periodic properties associated with the before unknown location of the maximum coefficient of these polynomials with odd n. Remarkably, the observed period is 62,624.

    更新日期:2020-07-06
  • Experimenting with Symplectic Hypergeometric Monodromy Groups
    Exp. Math. (IF 0.659) Pub Date : 2020-06-27
    A. S. Detinko; D. L. Flannery; A. Hulpke

    We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by extending our earlier algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties.

    更新日期:2020-06-27
  • A SAGE Package for n-Gonal Equisymmetric Stratification of
    Exp. Math. (IF 0.659) Pub Date : 2020-06-12
    Antonio Behn; Anita M. Rojas; Miguel Tello-Carrera

    In this work, we present an algorithm running over SAGE, which allows users to deal with group actions on Riemann surfaces up to topological equivalence. Our algorithm allows us to study the equisymmetric stratification of the branch locus Bg of the moduli space Mg of compact Riemann surfaces of genus g≥2, corresponding to group actions with orbit genus 0. That is, it works for actions on surfaces

    更新日期:2020-06-12
  • Platonic Solids and High Genus Covers of Lattice Surfaces
    Exp. Math. (IF 0.659) Pub Date : 2020-05-27
    Jayadev S. Athreya; David Aulicino; W. Patrick Hooper; with an appendix by Anja Randecker

    We study the translation surfaces obtained by considering the unfoldings of the surfaces of Platonic solids. We show that they are all lattice surfaces and we compute the topology of the associated Teichmüller curves. Using an algorithm that can be used generally to compute Teichmüller curves of translation covers of primitive lattice surfaces, we show that the Teichmüller curve of the unfolded dodecahedron

    更新日期:2020-05-27
  • Special Hypergeometric Motives and Their L-Functions: Asai Recognition
    Exp. Math. (IF 0.659) Pub Date : 2020-05-21
    Lassina Dembélé; Alexei Panchishkin; John Voight; Wadim Zudilin

    Abstract We recognize certain special hypergeometric motives, related to and inspired by the discoveries of Ramanujan more than a century ago, as arising from Asai L-functions of Hilbert modular forms.

    更新日期:2020-05-21
  • Frame Potential in CPn Some Numerical and Analytical Results
    Exp. Math. (IF 0.659) Pub Date : 2020-05-20
    Radel Ben Av; Giora Dula; Assaf Goldberger; Yossi Strassler

    In this paper we discuss minimizing a generalized frame potential - F(p,m,n) - for vectors in CPn. We discuss the minimal frame potential as well as the space of solutions for the minimization problem. We investigate this question both numerically and analytically. We find that for some values of p - Equiangular Tight Frames (ETF) are unique solutions, in contrast to the case of p = 2 where they are

    更新日期:2020-05-20
  • A Refined Conjecture for the Variance of Gaussian Primes across Sectors
    Exp. Math. (IF 0.659) Pub Date : 2020-05-01
    Ryan C. Chen; Yujin H. Kim; Jared D. Lichtman; Steven J. Miller; Alina Shubina; Shannon Sweitzer; Ezra Waxman; Eric Winsor; Jianing Yang

    We derive a refined conjecture for the variance of Gaussian primes across sectors, with a power saving error term, by applying the L-functions Ratios Conjecture. We observe a bifurcation point in the main term, consistent with the Random Matrix Theory (RMT) heuristic previously proposed by Rudnick and Waxman. Our model also identifies a second bifurcation point, undetected by the RMT model, that emerges

    更新日期:2020-05-01
  • Geodesic Nets: Some Examples and Open Problems
    Exp. Math. (IF 0.659) Pub Date : 2020-04-23
    Alexander Nabutovsky; Fabian Parsch

    Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean plane or the round 2-sphere. In the first part of this paper, we survey some results and open questions (old and new) about geodesic nets on Riemannian manifolds

    更新日期:2020-04-23
  • Embeddings of 3-Manifolds in S4 from the Point of View of the 11-Tetrahedron Census
    Exp. Math. (IF 0.659) Pub Date : 2020-04-16
    Ryan Budney; Benjamin A. Burton

    This is a collection of notes on embedding problems for 3-manifolds. The main question explored is “which 3-manifolds embed smoothly in S4?” The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed 3-manifolds built from 11 or less tetrahedra. There are 13766 manifolds in the census, of which 13400 are orientable. Of the 13400 orientable manifolds, only

    更新日期:2020-04-16
  • Superspecial Trigonal Curves of Genus 5
    Exp. Math. (IF 0.659) Pub Date : 2020-04-16
    Momonari Kudo; Shushi Harashita

    In this paper, we enumerate superspecial trigonal curves of genus 5 over Fpa for any natural number a if p≤7 and for odd a if p≤13. This paper provides an algorithm enumerating superspecial trigonal curves of genus 5 over Fq for arbitrary q. We implemented the algorithm over computer algebra system Magma. With help of computational results obtained by our implementation, we prove the nonexistence (resp

    更新日期:2020-04-16
  • Orthogonal Polynomials Defined by Self-Similar Measures with Overlaps
    Exp. Math. (IF 0.659) Pub Date : 2020-04-10
    Sze-Man Ngai; Wei Tang; Anh Tran; Shuai Yuan

    We study orthogonal polynomials with respect to self-similar measures, focusing on the class of infinite Bernoulli convolutions, which are defined by iterated function systems with overlaps, especially those defined by the Pisot, Garsia, and Salem numbers. By using an algorithm of Mantica, we obtain graphs of the coefficients of the 3-term recursion relation defining the orthogonal polynomials. We

    更新日期:2020-04-10
  • On Odd Torsion in Even Khovanov Homology
    Exp. Math. (IF 0.659) Pub Date : 2020-04-03
    Sujoy Mukherjee

    This short note resolves the most important part of the PS braid conjecture while introducing the first known examples of knots and links with odd torsion of order 9, 27, 81, and 25 in their even Khovanov homology.

    更新日期:2020-04-03
  • Spectral Properties of Laplacians on Snowflake Domains and Filled Julia Sets
    Exp. Math. (IF 0.659) Pub Date : 2020-03-26
    Robert S. Strichartz; Samuel C. Wiese

    We present eigenvalue data and pictures of eigenfunctions of the classic and quadratic snowflake fractal and of quadratic filled Julia sets. Furthermore, we approximate the area and box-counting dimension of selected Julia sets to compare the eigenvalue counting function with the Weyl term.

    更新日期:2020-03-26
  • Probabilistic Saturations and Alt’s Problem
    Exp. Math. (IF 0.659) Pub Date : 2020-03-26
    Jonathan D. Hauenstein; Martin Helmer

    Alt’s problem, formulated in 1923, is to count the number of four-bar linkages whose coupler curve interpolates nine general points in the plane. This problem can be phrased as counting the number of solutions to a system of polynomial equations which was first solved numerically using homotopy continuation by Wampler, Morgan, and Sommese in 1992. Since there is still not a proof that all solutions

    更新日期:2020-03-26
  • Generalizations of Hirschhorn’s Results on Two Remarkable q-Series Expansions
    Exp. Math. (IF 0.659) Pub Date : 2020-03-24
    Ernest X. W. Xia; Alice X. H. Zhao

    Recently, Hirschhorn investigated vanishing coefficients of the arithmetic progressions in the following two q-series expansions ∑n=0∞a(n)qn:=∏n=1∞(1+q5n−4)(1+q5n−1)(1−q10n−9)3(1−q10n−1)3,∑n=0∞b(n)qn:=∏n=1∞(1+q5n−3)(1+q5n−2)(1−q10n−7)3(1−q10n−3)3. He proved that for n≥0,a(5n+2)=a(5n+4)=b(5n+1)=b(5n+4)=0. In this paper, we further study these two q-series expansions and obtain the generating functions

    更新日期:2020-03-24
  • Four Lines and a Rectangle
    Exp. Math. (IF 0.659) Pub Date : 2020-03-18
    Richard Evan Schwartz

    This paper presents some configuration theorems concerning rectangles inscribed in four lines.

    更新日期:2020-03-18
  • The Doubly Stochastic Single Eigenvalue Problem: A Computational Approach
    Exp. Math. (IF 0.659) Pub Date : 2020-03-10
    Amit Harlev; Charles R. Johnson; Derek Lim

    The problem of determining DSn, the complex numbers that occur as an eigenvalue of an n-by-n doubly stochastic matrix, has been a target of study for some time. The Perfect-Mirsky region, PMn, is contained in DSn and is known to be exactly DSn for n≤4, but strictly contained within DSn for n = 5. Here, we present a Boundary Conjecture that asserts that the boundary of DSn is achieved by eigenvalues

    更新日期:2020-03-10
  • Minuscule Doppelgängers, The Coincidental down-Degree Expectations Property, and Rowmotion
    Exp. Math. (IF 0.659) Pub Date : 2020-03-05
    Sam Hopkins

    We relate Reiner, Tenner, and Yong’s coincidental down-degree expectations (CDE) property of posets to the minuscule doppelgänger pairs studied by Hamaker, Patrias, Pechenik, and Williams. Via this relation, we put forward a series of conjectures which suggest that the minuscule doppelgänger pairs behave “as if” they had isomorphic comparability graphs, even though they do not. We further explore the

    更新日期:2020-03-05
  • Determining the Trisection Genus of Orientable and Non-Orientable PL 4-Manifolds through Triangulations
    Exp. Math. (IF 0.659) Pub Date : 2020-03-05
    Jonathan Spreer; Stephan Tillmann

    Gay and Kirby recently introduced the concept of a trisection for arbitrary smooth, oriented closed 4-manifolds, and with it a new topological invariant, called the trisection genus. This paper improves and implements an algorithm due to Bell, Hass, Rubinstein and Tillmann to compute trisections using triangulations, and extends it to non-orientable 4–manifolds. Lower bounds on trisection genus are

    更新日期:2020-03-05
  • Construction of Acylindrical Hyperbolic 3-Manifolds with Quasifuchsian Boundary
    Exp. Math. (IF 0.659) Pub Date : 2020-03-05
    Yongquan Zhang

    We construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold, compute some associated arithmetic invariants and exhibit the skinning map along the deformation locus. The key idea is to construct a one-dimensional family of hyperbolic polyhedra; reflections in some of the faces of the polyhedra then generate a family of Kleinian groups.

    更新日期:2020-03-05
  • A Discrete Extrinsic and Intrinsic Dirac Operator
    Exp. Math. (IF 0.659) Pub Date : 2020-03-03
    Tim Hoffmann; Zi Ye

    In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavor (that comes with spin transformations to comformally transfrom immersions) and the two are naturally related. In this paper we consider a corresponding pair of discrete Dirac operators, the latter on discrete surfaces with polygonal faces and normals

    更新日期:2020-03-03
  • Weights, Weyl-Equivariant Maps and a Rank Conjecture
    Exp. Math. (IF 0.659) Pub Date : 2020-01-27
    Joseph Malkoun

    In this note, given a pair (g,λ), where g is a complex semisimple Lie algebra and λ∈h* is a dominant integral weight of g, where h⊂g is the real span of the coroots inside a fixed Cartan subalgebra, we associate an SU(2) and Weyl equivariant smooth map f:X→(Pm(C))n, where X⊂h⊗R3 is the configuration space of regular triples in h, and m, n depend on the initial data (g,λ). We conjecture that, for any

    更新日期:2020-01-27
  • Searching for Hyperbolic Polynomials with Span Less than 4
    Exp. Math. (IF 0.659) Pub Date : 2020-01-11
    Stefano Capparelli; Alberto Del Fra; Andrea Vietri

    A monic, irreducible polynomial in one variable having integer coefficients and all real roots deserves particular interest if its roots lie in an interval of length 4 whose end-points are not integers. This follows by some pioneering studies by R. Robinson. Thanks to the crucial support of computers, a number of contributions over the decades settled the existence question for such polynomials up

    更新日期:2020-01-11
  • Experiments with the Markoff Surface
    Exp. Math. (IF 0.659) Pub Date : 2020-01-10
    Matthew de Courcy-Ireland; Seungjae Lee

    We confirm, for the primes up to 3000, the conjecture of Bourgain-Gamburd-Sarnak and Baragar on strong approximation for the Markoff surface x2+y2+z2=3xyz modulo primes. For primes congruent to 3 modulo 4, we find data suggesting that some natural graphs constructed from this equation are asymptotically Ramanujan. For primes congruent to 1 modulo 4, the data suggest a weaker spectral gap. In both cases

    更新日期:2020-01-10
  • Finite Partitions for Several Complex Continued Fraction Algorithms
    Exp. Math. (IF 0.659) Pub Date : 2020-01-10
    Adam Abrams

    We present a property satisfied by a large variety of complex continued fraction algorithms (the “finite building property”) and use it to explore the structure of bijectivity domains for natural extensions of Gauss maps. Specifically, we show that these domains can each be given as a finite union of Cartesian products in C×C. In one complex coordinate, the sets come from explicit manipulation of the

    更新日期:2020-01-10
  • Numerically Destabilizing Minimal Discs
    Exp. Math. (IF 0.659) Pub Date : 2019-12-20
    Nicholas Brubaker; Thomas Murphy; K. Oskar Negron

    When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. We show that the set of admissible variations can be widened in a geometrically meaningful manner leading to a more general notion of index. This allows us to produce explicit examples of destabilizing perturbations for the fundamental

    更新日期:2019-12-20
  • Absolute Root Separation
    Exp. Math. (IF 0.659) Pub Date : 2019-12-18
    Yann Bugeaud; Andrej Dujella; Wenjie Fang; Tomislav Pejković; Bruno Salvy

    The absolute separation of a polynomial is the minimum nonzero difference between the absolute values of its roots. In the case of polynomials with integer coefficients, it can be bounded from below in terms of the degree and the height (the maximum absolute value of the coefficients) of the polynomial. We improve the known bounds for this problem and related ones. Then we report on extensive experiments

    更新日期:2019-12-18
  • Correction
    Exp. Math. (IF 0.659) Pub Date : 2019-12-04

    (2019). Correction. Experimental Mathematics. Ahead of Print.

    更新日期:2019-12-04
  • Serre’s Constant of Elliptic Curves Over the Rationals
    Exp. Math. (IF 0.659) Pub Date : 2019-12-02
    Harris B. Daniels; Enrique González-Jiménez

    Let E be an elliptic curve without complex multiplication defined over the rationals. The purpose of this article is to define a positive integer A(E), that we call the Serre’s constant associated to E, that gives necessary conditions to conclude that ρE,m, the mod m Galois representation associated to E, is non-surjective. In particular, if there exists a prime factor p of m satisfying valp(m)≥valp(A(E))>0

    更新日期:2019-12-02
  • Applications of Integer Semi-Infinite Programing to the Integer Chebyshev Problem
    Exp. Math. (IF 0.659) Pub Date : 2019-11-26
    Kevin G. Hare; Philip W. Hodges

    We consider the integer Chebyshev problem, that of minimizing the supremum norm over polynomials with integer coefficients on the interval [0, 1]. We implement algorithms from semi-infinite programing and a branch and bound algorithm to improve on previous methods for finding integer Chebyshev polynomials of degree n. Using our new method, we found 16 new integer Chebyshev polynomials of degrees in

    更新日期:2019-11-26
  • An Explicit Abelian Surface with Maximal Galois Action
    Exp. Math. (IF 0.659) Pub Date : 2019-11-25
    Quinn Greicius; Aaron Landesman

    We construct an explicit example of a genus 2 curve C over a number field K such that the adelic Galois representation arising from the action of Gal(K¯/K) on the Jacobian of C has image GSp4(Ẑ).

    更新日期:2019-11-25
  • On the Structure and Slopes of Drinfeld Cusp Forms
    Exp. Math. (IF 0.659) Pub Date : 2019-11-25
    Andrea Bandini; Maria Valentino

    We define oldforms and newforms for Drinfeld cusp forms of level t and conjecture that their direct sum is the whole space of cusp forms. Moreover we describe explicitly the matrix U associated to the action of the Atkin operator Ut on cusp forms of level t and use it to compute tables of slopes of eigenforms. Building on such data, we formulate conjectures on bounds for slopes, on the diagonalizability

    更新日期:2019-11-25
  • Rationality Proofs by Curve Counting
    Exp. Math. (IF 0.659) Pub Date : 2019-11-22
    Anton Mellit

    Abstract We propose an approach for showing rationality of an algebraic variety X. We try to cover X by rational curves of certain type and count how many curves pass through a generic point. If the answer is 1, then we can sometimes reduce the question of rationality of X to the question of rationality of a closed subvariety of X. This approach is applied to the case of the so-called Ueno-Campana

    更新日期:2019-11-22
  • On Some Average Properties of Convex Mosaics
    Exp. Math. (IF 0.659) Pub Date : 2019-11-21
    Gábor Domokos; Zsolt Lángi

    Abstract In a convex mosaic in Rd we denote the average number of vertices of a cell by v¯ and the average number of cells meeting at a node by n¯. Except for the d = 2 planar case, there is no known formula prohibiting points in any range of the [n¯,v¯] plane (except for the unphysical n¯,v¯

    更新日期:2019-11-21
  • Computer-Aided Study of Double Extensions of Restricted Lie Superalgebras Preserving the Nondegenerate Closed 2-Forms in Characteristic 2
    Exp. Math. (IF 0.659) Pub Date : 2019-11-18
    Sofiane Bouarroudj; Dimitry Leites; Jin Shang

    A Lie (super)algebra with a nondegenerate invariant symmetric bilinear form B is called a nis-(super)algebra. The double extension g of a nis-(super)algebra a is the result of simultaneous adding to a a central element and a derivation so that g is a nis-algebra. Loop algebras with values in simple complex Lie algebras are most known among the Lie (super)algebras suitable to be doubly extended. In

    更新日期:2019-11-18
  • The Expansion ⋆ mod ō (ℏ4) and Computer-Assisted Proof Schemes in the Kontsevich Deformation Quantization
    Exp. Math. (IF 0.659) Pub Date : 2019-11-18
    R. Buring; A. V. Kiselev

    The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these allow generating the Kontsevich graphs, expanding the noncommutative ⋆-product by using a priori undetermined coefficients, and deriving linear relations

    更新日期:2019-11-18
  • Generalized Samuel Multiplicities of Monomial Ideals and Volumes
    Exp. Math. (IF 0.659) Pub Date : 2019-11-07
    Rüdiger Achilles; Mirella Manaresi

    We describe conjecturally the generalized Samuel multiplicities c0,…,cd−1 of a monomial ideal I⊂K[x1,…,xd] in terms of its Newton polyhedron NP(I). More precisely, we conjecture that ci equals the sum of the normalized (d−i)-volumes of pyramids over the projections of the (d−i−1)-dimensional compact faces of NP(I) along the infinite-directions of i-unbounded facets in which they are contained. For

    更新日期:2019-11-07
  • Note on the Cyclotomic Polynomial Topologically
    Exp. Math. (IF 0.659) Pub Date : 2019-11-01
    Aleksandra Kostić; Nela Milošević; Zoran Z. Petrović

    Coefficients of the cyclotomic polynomial can be interpreted topologically, as the torsion in the homology of a certain simplicial complex associated with the degree of the cyclotomic polynomial, which was studied by Musiker and Reiner. We answer a question posed by the two authors regarding homotopy type of certain subcomplexes of the associated simplicial complex when the degree of the cyclotomic

    更新日期:2019-11-01
  • Fingering in Stochastic Growth Models.
    Exp. Math. (IF 0.659) Pub Date : 2014-01-01
    Andreas C Aristotelous,Richard Durrett

    Motivated by the widespread use of hybrid-discrete cellular automata in modeling cancer, two simple growth models are studied on the two dimensional lattice that incorporate a nutrient, assumed to be oxygen. In the first model the oxygen concentration u(x, t) is computed based on the geometry of the growing blob, while in the second one u(x, t) satisfies a reaction-diffusion equation. A threshold θ

    更新日期:2019-11-01
  • Non-Existence and Finiteness Results for Teichmüller Curves in Prym Loci
    Exp. Math. (IF 0.659) Pub Date : 2019-10-16
    Erwan Lanneau; Martin Möller

    The minimal stratum in Prym loci have been the first source of infinitely many primitive, but not algebraically primitive Teichmüller curves. We show that the stratum Prym(1, 2) contains no such Teichmüller curve and the stratum Prym(2) at most 92 such Teichmüller curves. This complements the recent progress establishing general – but non-effective – methods to prove finiteness results for Teichmüller

    更新日期:2019-10-16
  • On q-Deformed Real Numbers
    Exp. Math. (IF 0.659) Pub Date : 2019-10-08
    Sophie Morier-Genoud; Valentin Ovsienko

    We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a “q-analogue of a real.” The construction is based on the notion of q-deformed rational number introduced in arXiv:1812.00170. Extending the construction to negative real numbers, we obtain certain Laurent series.

    更新日期:2019-10-08
  • An Investigation Into the Cyclically Presented Groups with Length Three Positive Relators
    Exp. Math. (IF 0.659) Pub Date : 2019-09-25
    Esamaldeen Mohamed; Gerald Williams

    We continue research into the cyclically presented groups with length three positive relators. We study small cancelation conditions, SQ-universality, and hyperbolicity, we obtain the Betti numbers of the groups’ abelianisations, we calculate the orders of the abelianisations of some groups, and we study isomorphism classes of the groups. Through computational experiments we assess how effective the

    更新日期:2019-09-25
  • A Markov Chain Sampler for Plane Curves
    Exp. Math. (IF 0.659) Pub Date : 2019-09-23
    Harrison Chapman; Andrew Rechnitzer

    A plane curve is a knot diagram in which each crossing is replaced by a 4-valent vertex, and so are dual to a subset of planar quadrangulations. The aim of this article is to introduce a new tool for sampling diagrams via sampling of plane curves. At present the most efficient method for sampling diagrams is rejection sampling, however that method is inefficient at even modest sizes. We introduce Markov

    更新日期:2019-09-23
  • Cyclotomic Coincidences
    Exp. Math. (IF 0.659) Pub Date : 2019-09-17
    Carl Pomerance; Simon Rubinstein-Salzedo

    Let Φn denotes the nth cyclotomic polynomial. In this paper, we show that if m and n are distinct positive integers and x is a nonzero real number with Φm(x)=Φn(x), then 12<|x|<2 except when {m,n}={2,6} and x = 2. We also observe that 2 appears to be the largest real limit point of the set of values of x for which Φm(x)=Φn(x) for some m≠n.

    更新日期:2019-09-17
  • On Two Truncated Quintuple Series Theorems
    Exp. Math. (IF 0.659) Pub Date : 2019-09-17
    Mircea Merca

    We investigate two truncated series derived recently by S. H. Chan, T. P. N. Ho, and R. Mao from the Watson quintuple product identity and experimentally discover two stronger results. In this context, for each S∈{1,2}, we obtain two infinite families of linear homogeneous inequalities for the number of partitions of n into parts congruent to ±Smod5.

    更新日期:2019-09-17
  • The Graph Curvature Calculator and the Curvatures of Cubic Graphs
    Exp. Math. (IF 0.659) Pub Date : 2019-09-14
    David Cushing; Riikka Kangaslampi; Valtteri Lipiäinen; Shiping Liu; George W. Stagg

    We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-Émery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the Möbius ladders. As a consequence of the classification result we show that non-negatively curved cubic expanders do not exist. We also introduce the Graph Curvature Calculator

    更新日期:2019-09-14
  • Computational Explorations of the Thompson Group T for the Amenability Problem of F
    Exp. Math. (IF 0.659) Pub Date : 2019-08-30
    Søren Haagerup; Uffe Haagerup; Maria Ramirez-Solano

    It is a long standing open problem whether the Thompson group F is an amenable group. In this article, we show that if A, B, C denote the standard generators of Thompson group T and D:=CBA−1 then 2+3 < 112||(I+C+C2)(I+D+D2+D3)|| ≤ 2+2.Moreover, the upper bound is attained if the Thompson group F is amenable. Here, the norm of an element in the group ring CT is computed in B(ℓ2(T)) via the regular representation

    更新日期:2019-08-30
  • Real Inflection Points of Real Linear Series on an Elliptic Curve
    Exp. Math. (IF 0.659) Pub Date : 2019-08-26
    Ethan Cotterill; Cristhian Garay López

    Given a real elliptic curve E with non-empty real part and a real effective divisor D on E arising via pullback from P1 under the hyperelliptic structure map, we study the real inflection points of distinguished subseries of the complete real linear series |D| on E. We define inflection polynomials whose roots index the (x-coordinates of) inflection points of the linear series, away from the points

    更新日期:2019-08-26
  • Asymptotic Sign Coherence Conjecture
    Exp. Math. (IF 0.659) Pub Date : 2019-08-21
    Michael Gekhtman; Tomoki Nakanishi

    The sign coherence phenomenon is an important feature of c-vectors in cluster algebras with principal coefficients. In this note, we consider a more general version of c-vectors defined for arbitrary cluster algebras of geometric type and formulate a conjecture describing their asymptotic behavior. This conjecture, which is called the asymptotic sign coherence conjecture, states that for any infinite

    更新日期:2019-08-21
  • The Optimal Packing of Eight Points in the Real Projective Plane
    Exp. Math. (IF 0.659) Pub Date : 2019-07-27
    Dustin G. Mixon; Hans Parshall

    How can we arrange n lines through the origin in three-dimensional Euclidean space in a way that maximizes the minimum interior angle between pairs of lines? Conway, Hardin, and Sloane (1996) produced line packings for n≤55 that they conjectured to be within numerical precision of optimal in this sense, but until now only the cases n≤7 have been solved. In this paper, we resolve the case n = 8. Drawing

    更新日期:2019-07-27
  • Extremal Cylinder Configurations II: Configuration O6
    Exp. Math. (IF 0.659) Pub Date : 2019-07-22
    Oleg Ogievetsky; Senya Shlosman

    We study the octahedral configuration O6 [Kuperberg] of six equal cylinders touching the unit sphere. We show that the configuration O6 is a local sharp maximum of the distance function. Thus, it is not unlockable and, moreover, rigid.

    更新日期:2019-07-22
  • Topological Prismatoids and Small Simplicial Spheres of Large Diameter
    Exp. Math. (IF 0.659) Pub Date : 2019-07-22
    Francisco Criado; Francisco Santos

    We introduce topological prismatoids, a combinatorial abstraction of the (geometric) prismatoids recently introduced by the second author to construct counter-examples to the Hirsch conjecture. We show that the “strong d-step Theorem” that allows to construct such large-diameter polytopes from “non-d-step” prismatoids still works at this combinatorial level. Then, using metaheuristic methods on the

    更新日期:2019-07-22
  • The Fuglede Conjecture Holds in
    Exp. Math. (IF 0.659) Pub Date : 2019-07-12
    Philipp Birklbauer

    The Fuglede conjecture states that a set is spectral if and only if it tiles by translation. The conjecture was disproved by Tao for dimensions 5 and higher by giving a counterexample in Z35. We present a computer program that determines that the Fuglede conjecture holds in Z35 by exhausting the search space. Recently Iosevich, Mayeli and Pakianathan showed that the Fuglede conjecture holds over prime

    更新日期:2019-07-12
  • On Integers that are Covering Numbers of Groups
    Exp. Math. (IF 0.659) Pub Date : 2019-07-12
    Martino Garonzi; Luise-Charlotte Kappe; Eric Swartz

    The covering number of a group G, denoted by σ(G), is the size of a minimal collection of proper subgroups of G whose union is G. We investigate which integers are covering numbers of groups. We determine which integers 129 or smaller are covering numbers, and we determine precisely or bound the covering number of every primitive monolithic group with a degree of primitivity at most 129 by introducing

    更新日期:2019-07-12
  • The Reidemeister Spectra of Low Dimensional Almost-Crystallographic Groups
    Exp. Math. (IF 0.659) Pub Date : 2019-07-11
    Sam Tertooy

    We determine which non-crystallographic, almost-crystallographic groups of dimension-4 have the R∞-property. We then calculate the Reidemeister spectra of the 3-dimensional almost-crystallographic groups and the 4-dimensional almost-Bieberbach groups.

    更新日期:2019-07-11
  • Discovering and Proving Infinite Pochhammer Sum Identities
    Exp. Math. (IF 0.659) Pub Date : 2019-07-01
    Jakob Ablinger

    Abstract We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of π, log (2), or zeta values. In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals or directly in

    更新日期:2019-07-01
  • Lattice-Packing by Spheres and Eutactic Forms
    Exp. Math. (IF 0.659) Pub Date : 2019-06-26
    Avner Ash; Robert Gross

    We consider a semi-random walk on the space X of lattices in Euclidean n-space which attempts to maximize the sphere-packing density function Φ. A lattice (or its corresponding quadratic form) is called “sticky” if the set of directions in X emanating from it along which Φ is infinitesimally increasing has measure 0 in the set of all directions. Thus the random walk will tend to get “stuck” in the

    更新日期:2019-06-26
  • Quantum Periods for Certain Four-Dimensional Fano Manifolds
    Exp. Math. (IF 0.659) Pub Date : 2018-08-29
    Tom Coates; Sergey Galkin; Alexander Kasprzyk; Andrew Strangeway

    ABSTRACT We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all four-dimensional toric Fano manifolds, all four-dimensional products of lower-dimensional Fano manifolds, and certain complete intersections in projective bundles.

    更新日期:2018-08-29
  • Commensurability and Arithmetic Equivalence for Orthogonal Hypergeometric Monodromy Groups
    Exp. Math. (IF 0.659) Pub Date : 2018-05-08
    Jitendra Bajpai; Sandip Singh; Scott Thomson

    Invariants are computed of quadratic forms associated with orthogonal hypergeometric groups of degree five. Some commensurabilities are then determined between these groups, and it is established that some thin groups cannot be conjugated to each other.

    更新日期:2018-05-08
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
欢迎访问IOP中国网站
自然职场线上招聘会
GIANT
产业、创新与基础设施
自然科研线上培训服务
材料学研究精选
胸腔和胸部成像专题
屿渡论文,编辑服务
何川
苏昭铭
陈刚
姜涛
李闯创
李刚
北大
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
天合科研
x-mol收录
上海纽约大学
陈芬儿
厦门大学
何振宇
史大永
吉林大学
卓春祥
张昊
杨中悦
试剂库存
down
wechat
bug