-
Hall’s universal group is a subgroup of the abstract commensurator of a free group Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Edgar A. Bering, Daniel Studenmund
P. Hall constructed a universal countable locally finite group U, determined up to isomorphism by two properties: every finite group C is a subgroup of U, and every embedding of C into U is conjugate in U. Every countable locally finite group is a subgroup of U. We prove that U is a subgroup of the abstract commensurator of a finite-rank nonabelian free group.
-
Probabilistic hypergraph containers Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Rajko Nenadov
Given a k-uniform hypergraph ℋ and sufficiently large m ≫ m0(ℋ), we show that an m-element set I ⊆ V(ℋ), chosen uniformly at random, with probability 1 − e−ω(m) is either not independent or is contained in an almost-independent set in ℋ which, crucially, can be constructed from carefully chosen o(m) vertices of I. As a corollary, this implies that if the largest almost-independent set in ℋ is of size
-
Topological characterizations of recurrence, Poisson stability, and isometric property of flows on surfaces Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Tomoo Yokoyama
The long-time behavior is one of the most fundamental properties of dynamical systems. Poincaré studied the Poisson stability to capture the property of whether points return arbitrarily near the initial positions. Birkhoff studied the concept of recurrent points. Hilbert introduced distal property to describe a rigid group of motions. We show that Poisson stability, recurrence, and distal property
-
On parabolic subgroups of Artin groups Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Philip Möller, Luis Paris, Olga Varghese
Given an Artin group AΓ, a common strategy in the study of AΓ is the reduction to parabolic subgroups whose defining graphs have small diameter, i.e., showing that AΓ has a specific property if and only if all “small” parabolic subgroups of AΓ have this property. Since “small” parabolic subgroups are the building blocks of AΓ one needs to study their behavior, in particular their intersections. The
-
Locally harmonic Maass forms of positive even weight Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Andreas Mono
We twist Zagier’s function fk,D by a sign function and a genus character. Assuming weight 0 < k ≡ 2 (mod 4), and letting D be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign function can be corrected obtaining a locally harmonic Maaß form or a local cusp form of the same weight. In addition, we provide an alternative representation of our new function
-
Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Pablo D. Carrasco, Federico Rodriguez-Hertz
We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with Hölder Jacobians. In the same setting, we give a precise characterization of the equilibrium states of the hyperbolic system, showing that existence of a family of Radon measures on the horocyclic foliation such that any probability
-
On the packing/covering conjecture of infinite matroids Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Attila Joó
The Packing/Covering Conjecture was introduced by Bowler and Carmesin motivated by the Matroid Partition Theorem of Edmonds and Fulkerson. A packing for a family \(({M_i}:i \in \Theta)\) of matroids on the common edge set E is a system \(({S_i}:i \in \Theta)\) of pairwise disjoint subsets of E where Si is panning in Mi. Similarly, a covering is a system (Ii: i ∈ Θ) with \({\cup _{i \in \Theta}}{I_i}
-
Longest increasing path within the critical strip Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Partha S. Dey, Mathew Joseph, Ron Peled
A Poisson point process of unit intensity is placed in the square [0, n]2. An increasing path is a curve connecting (0, 0) with (n, n) which is non-decreasing in each coordinate. Its length is the number of points of the Poisson process which it passes through. Baik, Deift and Johansson proved that the maximal length of an increasing path has expectation 2n − n1/3(c1 + o(1)), variance n2/3(c2 + o(1))
-
Waring–Goldbach problem in short intervals Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Mengdi Wang
Let k ≥ 2 and s be positive integers. Let θ ∈ (0, 1) be a real number. In this paper, we establish that if s > k(k + 1) and θ > 0.55, then every sufficiently large natural number n, subject to certain congruence conditions, can be written as $$n = p_1^k + \cdots + p_s^k,$$ , where pi (1 ≤ i ≤ s) are primes in the interval \(({({n \over s})^{{1 \over k}}} - {n^{{\theta \over k}}},{({n \over s})^{{1
-
Symplectic instability of Bézout’s theorem Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18
Abstract We investigate the failure of Bézout’s Theorem for two symplectic surfaces in ℂP2 (and more generally on an algebraic surface), by proving that every plane algebraic curve C can be perturbed in the \({{\cal C}^\infty }\) -topology to an arbitrarily close smooth symplectic surface Cϵ with the property that the cardinality #Cϵ ∩ Zd of the transversal intersection of Cϵ with an algebraic plane
-
Bökstedt periodicity generator via K-theory Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Anton Fonarev, Dmitry Kaledin
For a prime field k of characteristic p > 2, we construct the Bökstedt periodicity generator v ∈ THH2(k) as an explicit class in the stabilization of K-theory with coefficients K(k, −), and we show directly that v is not nilpotent in THH(k). This gives an alternative proof of the “multiplicative” part of Bökstedt periodicity.
-
On uniqueness and plentitude of subsymmetric sequences Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Peter G. Casazza, Stephen J. Dilworth, Denka Kutzarova, Pavlos Motakis
We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(T*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent
-
Short homology bases for hyperelliptic hyperbolic surfaces Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Peter Buser, Eran Makover, Bjoern Muetzel
Given a hyperelliptic hyperbolic surface S of genus g ≥ 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any λ ∈ (0, 1) there exists a constant N(λ) such that every such surface has at least \(\left\lceil {\lambda \cdot {2 \over 3}g} \right\rceil \) homologically independent loops of length at most N(λ), extending the result in [Mu] and [BPS]
-
A remark on discrete Brunn–Minkowski type inequalities via transportation of measure Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Boaz A. Slomka
We give an alternative proof for discrete Brunn–Minkowski type inequalities, recently obtained by Halikias, Klartag and the author. This proof also implies somewhat stronger weighted versions of these inequalities. Our approach generalizes ideas of Gozlan, Roberto, Samson and Tetali from the theory of measure transportation and provides new displacement convexity of entropy type inequalities on the
-
Effective Hilbert’s irreducibility theorem for global fields Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Marcelo Paredes, Román Sasyk
We prove an effective form of Hilbert’s irreducibility theorem for polynomials over a global field K. More precisely, we give effective bounds for the number of specializations \(t \in {{\cal O}_K}\) that do not preserve the irreducibility or the Galois group of a given irreducible polynomial F(T, Y) ∈ K[T, Y]. The bounds are explicit in the height and degree of the polynomial F(T, Y), and are optimal
-
Simplifying matrix differential equations with general coefficients Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18
Abstract We show that the n × n matrix differential equation δ(Y) = AY with n2 general coefficients cannot be simplified to an equation in less than n parameters by using gauge transformations whose coefficients are rational functions in the matrix entries of A and their derivatives. Our proof uses differential Galois theory and a differential analogue of essential dimension. We also bound the minimum
-
Modular phenomena for regularized double zeta values Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Minoru Hirose
In this paper, we investigate linear relations among regularized motivic iterated integrals on ℙ1 ∖ {0, 1, ∞} of depth two, which we call regularized motivic double zeta values. Some mysterious connections between motivic multiple zeta values and modular forms are known, e.g., Gangl–Kaneko–Zagier relation for the totally odd double zeta values and Ihara–Takao relation for the depth graded motivic Lie
-
Bernoullicity of lopsided principal algebraic actions Isr. J. Math. (IF 1.0) Pub Date : 2023-12-18 Hanfeng Li, Kairan Liu
We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bernoulli.
-
Lifting (co)stratifications between tensor triangulated categories Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Liran Shaul, Jordan Williamson
We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact R-linear functor between R-linear tensor-triangulated categories which are rigidly-compactly generated by their tensor units. We then apply these results to non-positive commutative DG-rings and connective ring spectra. In particular, this gives a support-theoretic
-
Polynomial growth of the codimensions sequence of algebras with group graded involution Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Maralice Assis de Oliveira, Rafael Bezerra dos Santos, Ana Cristina Vieira
An algebra graded by a group G and endowed with a graded involution * is called a (G, *)-algebra. Here we consider G a finite abelian group and classify the subvarieties of the varieties of almost polynomial growth generated by finite-dimensional (G, *)-algebras. Also, we present, up to equivalence, the complete list of (G, *)-algebras generating varieties of at most linear growth. Along the way, we
-
Orbit configuration spaces and the homotopy groups of the pair $$(\prod\nolimits_1^n {M,{F_n}} (M))$$ for M either $${\mathbb{S}^2}$$ or ℝP2 Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Daciberg Lima Gonçalves, John Guaschi
Let n ≥ 1, and let \({\iota _n}:{F_n}(M) \to \prod\nolimits_1^n M \) be the natural inclusion of the nth configuration space of M in the n-fold Cartesian product of M with itself. In this paper, we study the map ιn, the homotopy fibre In of ιn and its homotopy groups, and the induced homomorphisms (ιn)#k on the kth homotopy groups of Fn(M) and \(\prod\nolimits_1^n M \) for all k ≥ 1, where M is the
-
On the mean radius of quasiconformal mappings Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Alastair N. Fletcher, Jacob Pratscher
We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in ℝn, for n ≥ 2, called bounded integrable parameterization mappings, or BIP maps for short. These have the property that the restriction of the Zorich transform to each slice has uniformly bounded derivative in Ln/(n−1). For BIP maps, the logarithmic transform of the mean radius
-
Homology of the pronilpotent completion and cotorsion groups Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Mikhail Basok, Sergei O. Ivanov, Roman Mikhailov
For a non-cyclic free group F, the second homology of its pronilpotent completion \({H_2}(\widehat F)\) is not a cotorsion group.
-
Notes on restriction theory in the primes Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Olivier Ramaré
We study the mean \(\sum\nolimits_{x \in {\cal X}} {|\sum\nolimits_{p \le N} {{u_p}e(xp){|^\ell}}} \) when ℓ covers the full range [2, ∞) and \({\cal X} \subset \mathbb{R}/\mathbb{Z}\) is a well-spaced set, providing a smooth transition from the case ℓ = 2 to the case ℓ > 2 and improving on the results of J. Bourgain and of B. Green and T. Tao. A uniform Hardy–Littlewood property for the set of primes
-
On the Rankin–Selberg L-factors for SO5 × GL2 Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Yao Cheng
Let π and τ be irreducible smooth generic representations of SO5 and GL2 respectively over a non-archimedean local field. We show that the L- and ε-factors attached to π×π defined by the Rankin–Selberg integrals and the associated Weil–Deligne representation coincide. The proof is obtained by explicating the relation between the Rankin–Selberg integrals for SO5 × GL2 and Novodvorsky’s local integrals
-
The profinite completion of relatively hyperbolic virtually special groups Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Pavel Zalesskii
We give a characterization of toral relatively hyperbolic virtually special groups in terms of the profinite completion. We also prove a Tits alternative for subgroups of the profinite completion Ĝ of a relatively hyperbolic virtually compact special group G and completely describe finitely generated pro-p subgroups of Ĝ. This applies to the profinite completion of the fundamental group of a hyperbolic
-
The cube axiom and resolutions in homotopy theory Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Manfred Stelzer
We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model structure. As an application, classical theorems in unstable homotopy theory are extended to this context.
-
The newform K-type and p-adic spherical harmonics Isr. J. Math. (IF 1.0) Pub Date : 2023-11-29 Peter Humphries
Let \(K: = {\rm{G}}{{\rm{L}}_n}({\cal O})\) denote the maximal compact subgroup of GLn(F), where F is a nonarchimedean local field with ring of integers \({\cal O}\). We study the decomposition of the space of locally constant functions on the unit sphere in Fn into irreducible K-modules; for F = ℚp, these are the p-adic analogues of spherical harmonics. As an application, we characterise the newform
-
An infinite interval version of the α-Kakutani equidistribution problem Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Mark Pollicott, Benedict Sewell
In this article we extend results of Kakutani, Adler–Flatto, Smilansky and others on the classical α-Kakutani equidistribution result for sequences arising from finite partitions of the interval. In particular, we describe a generalization of the equidistribution result to infinite partitions. In addition, we give discrepancy estimates, extending results of Drmota–Infusino [8].
-
Immersion of complete digraphs in Eulerian digraphs Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 António Girão, Shoham Letzter
A digraph G immerses a digraph H if there is an injection f: V(H) → V(G) and a collection of pairwise edge-disjoint directed paths Puv, for uv ∈ E(H), such that Puv starts at f(u) and ends at f(v). We prove that every Eulerian digraph with minimum out-degree t immerses a complete digraph on Ω(t) vertices, thus answering a question of DeVos, McDonald, Mohar and Scheide.
-
Martin–Löf reducibility and cost functions Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Noam Greenberg, Joseph S. Miller, André Nies, Dan Turetsky
Martin—Löf (ML)-reducibility compares the complexity of K-trivial sets of natural numbers by examining the Martin—Löf random sequences that compute them. One says that a K-trivial set A is ML-reducible to a K-trivial set B if every ML-random computing B also computes A. We show that every K-trivial set is computable from a c.e. set of the same ML-degree. We investigate the interplay between ML-reducibility
-
The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Tara Brendle, Nathan Broaddus, Andrew Putman
We give two proofs that appropriately defined congruence subgroups of the mapping class group of a surface with punctures/boundary have enormous amounts of rational cohomology in their virtual cohomological dimension. In particular we give bounds that are super-exponential in each of three variables: number of punctures, number of boundary components, and genus, generalizing work of Fullarton–Putman
-
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Menachem Kojman, Assaf Rinot, Juris Steprāns
In this series of papers we advance Ramsey theory over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions that homogenize colorings over them is uncovered. At the level of the first uncountable cardinal this gives rise to a duality theorem under Martin’s Axiom: a function p: [ω1]2 → ω witnesses a weak negative
-
ℤ/pr-hyperbolicity via homology Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Guy Boyde
We show that the homotopy groups of a Moore space Pn(pr), where pr ≠ 2, are ℤ/ps-hyperbolic for s ≤ r. Combined with work of Huang–Wu, Neisendorfer, and Theriault, this completely resolves the question of when such a Moore space is ℤ/ps-hyperbolic for p ≥ 5, or when p = 2 and r ≥ 6. We also give a criterion in ordinary homology for a space to be ℤ/pr-hyperbolic, and deduce some examples.
-
Topological mixing of positive diagonal flows Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Nguyen-Thi Dang
Let G be a connected, real linear, semisimple Lie group without compact factors and Γ < G a Zariski dense, discrete subgroup. We study the topological dynamics of positive diagonal flows on ΓG. We extend Hopf coordinates to Bruhat–Hopf coordinates of G, which gives the framework to estimate the elliptic part of products of large generic loxodromic elements. By rewriting results of Guivarc’h–Raugi into
-
Conservation strength of the infinite pigeonhole principle for trees Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Chi Tat Chong, Wei Wang, Yue Yang
Let TT1 be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let RT 22 and WKL0 denote respectively the principles of Ramsey’s theorem for pairs and the weak König lemma. It is proved that TT1 + RT 22 + WKL0 is Π 03 -conservative over the base system RCA0. Thus over RCA0, TT1 and Ramsey’s theorem for pairs prove the
-
Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Menachem Kojman, Assaf Rinot, Juris Steprāns
In this series of papers we advance Ramsey theory over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in particular solve two problems from [CKS21]. It is shown that for every infinite cardinal λ, a strong coloring on λ+ by λ colors over a partition can be stretched to one with λ+ colors over the same partition. Also, a sufficient
-
Regularity results for local solutions to some anisotropic elliptic equations Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Giuseppina di Blasio, Filomena Feo, Gabriella Zecca
In this paper we study the higher integrability of local solutions for a class of anisotropic equations with lower order terms whose growth coefficients lay in Marcinkiewicz spaces. A condition for the boundedness of such solutions is also given.
-
The Galois action on the lower central series of the fundamental group of the Fermat curve Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Rachel Davis, Rachel Pries, Kirsten Wickelgren
Information about the absolute Galois group GK of a number field K is encoded in how it acts on the étale fundamental group π of a curve X defined over K. In the case that K = ℚ(ζn) is the cyclotomic field and X is the Fermat curve of degree n ≥ 3, Anderson determined the action of GK on the étale homology with coefficients in ℤ/nℤ. The étale homology is the first quotient in the lower central series
-
Wonderful compactifications of Bruhat–Tits buildings in the non-split case Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Dorian Chanfi
Given an adjoint semisimple group G over a local field k, we prove that the maximal Satake–Berkovich compactification of the Bruhat–Tits building of G can be identified with the one obtained by embedding the building into the Berkovich analytification of the wonderful compactification of G, extending previous results of Rémy, Thuillier and Werner. In the process, we use the characterisation of the
-
Topological speedups for minimal Cantor systems Isr. J. Math. (IF 1.0) Pub Date : 2023-11-13 Drew D. Ash, Nicholas S. Ormes
In this paper we study speedups of dynamical systems in the topological category. Specifically, we characterize when one minimal homeomorphism on a Cantor space is the speedup of another. We go on to provide a characterization for strong speedups, i.e., when the jump function has at most one point of discontinuity. These results provide topological versions of the measure-theoretic results of Arnoux
-
Multidimensional polynomial Szemerédi theorem in finite fields for polynomials of distinct degrees Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Borys Kuca
We obtain a polynomial upper bound in the finite-field version of the multidimensional polynomial Szemerédi theorem for distinct-degree polynomials. That is, if P1, …, Pt are nonconstant integer polynomials of distinct degrees and v1, …, vt are nonzero vectors in \(\mathbb{F}_p^D\), we show that each subset of \(\mathbb{F}_p^D\) lacking a nontrivial configuration of the form $${\bf{x}},{\bf{x}} +
-
Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Koichi Betsumiya, Ching Hung Lam, Hiroki Shimakura
We determine the automorphism groups of the cyclic orbifold vertex operator algebras associated with coinvariant lattices for isometries of the Leech lattice in the conjugacy classes 4C, 6E, 6G, 8E and 10F. As a consequence, we have determined the automorphism groups of all the 10 vertex operator algebras in [Hö], which are useful to analyze holomorphic vertex operator algebras of central charge 24
-
Hypergraphs with minimum positive uniform Turán density Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Frederik Garbe, Daniel Kráľ, Ander Lamaison
Reiher, Rödl and Schacht showed that the uniform Turán density of every 3-uniform hypergraph is either 0 or at least 1/27, and asked whether there exist 3-uniform hypergraphs with uniform Turán density equal or arbitrarily close to 1/27. We construct 3-uniform hypergraphs with uniform Turán density equal to 1/27.
-
Ergodic decompositions of geometric measures on Anosov homogeneous spaces Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Minju Lee, Hee Oh
Let G be a connected semisimple real algebraic group and Γ a Zariski dense Anosov subgroup of G with respect to a minimal parabolic subgroup P. Let N be the maximal horospherical subgroup of G given by the unipotent radical of P. We describe the N-ergodic decompositions of all Burger–Roblin measures as well as the A-ergodic decompositions of all Bowen–Margulis–Sullivan measures on ΓG. As a consequence
-
A modular idealizer chain and unrefinability of partitions with repeated parts Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Riccardo Aragona, Roberto Civino, Norberto Gavioli
Recently Aragona et al. have introduced a chain of normalizers in a Sylow 2-subgroup of Sym(2n), starting from an elementary abelian regular subgroup. They have shown that the indices of consecutive groups in the chain depend on the number of partitions into distinct parts and have given a description, by means of rigid commutators, of the first n − 2 terms in the chain. Moreover, they proved that
-
Bounded geometry with no bounded pants decomposition Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Ara Basmajian, Hugo Parlier, Nicholas G. Vlamis
We construct a quasiconformally homogeneous hyperbolic Riemann surface—other than the hyperbolic plane—that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact boundary components, we construct a complete hyperbolic metric on the surface that has bounded geometry but does not admit a bounded pants decomposition.
-
Discriminants of fields generated by polynomials of given height Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Rainer Dietmann, Alina Ostafe, Igor E. Shparlinski
We obtain upper bounds for the number of monic irreducible polynomials over \(\mathbb{Z}\) of a fixed degree n and a growing height H for which the field generated by one of its roots has a given discriminant. We approach it via counting square-free parts of polynomial discriminants via two complementing approaches. In turn, this leads to a lower bound on the number of distinct discriminants of fields
-
The parabolic algebra revisited Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Eleftherios Kastis, Stephen C. Power
The parabolic algebra \({{\cal A}_p}\) is the weakly closed operator algebra on \({L^2}(\mathbb{R})\) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions \({e^{i\lambda x}},\lambda \ge 0\). It is reflexive, with an invariant subspace lattice \({\rm{Lat}}{{\cal A}_p}\) which is naturally homeomorphic to the unit disc
-
Spectral sections Isr. J. Math. (IF 1.0) Pub Date : 2023-10-09 Marina Prokhorova
The paper is devoted to the notion of a spectral section introduced by Melrose and Piazza. In the first part of the paper we generalize results of Melrose and Piazza to arbitrary base spaces, not necessarily compact. The second part contains a number of special cases, including cobordism theorems for families of Dirac type operators parametrized by a non-compact base space. In the third part of the
-
Rainbow cycles for families of matchings Isr. J. Math. (IF 1.0) Pub Date : 2023-10-10 Ron Aharoni, He Guo
Given a graph G and a coloring of its edges, a subgraph of G is called rainbow if its edges have distinct colors. The rainbow girth of an edge coloring of G is the minimum length of a rainbow cycle in G. A generalization of the famous Caccetta–Häggkvist conjecture, proposed by the first author, is that if in a coloring of the edge set of an n-vertex graph by n colors, in which each color class is of
-
Good permutation codes based on the shuffle-exchange network Isr. J. Math. (IF 1.0) Pub Date : 2023-10-10 Oded Goldreich, Avi Wigderson
We consider the problem of efficiently constructing an as large as possible family of permutations such that each pair of permutations are far part (i.e., disagree on a constant fraction of their inputs). Specifically, for every n ∈ ℕ, we present a collection of N = N(n) = (n!)Ω(1) pairwise far apart permutations {πi: [n] → [n]}i∈[N] and a polynomial-time algorithm that on input i ∈ [N] outputs an
-
Attempting perfect hypergraphs Isr. J. Math. (IF 1.0) Pub Date : 2023-10-10 Maria Chudnovsky, Gil Kalai
We study several extensions of the notion of perfect graphs to k-uniform hypergraphs. One main definition extends to hypergraphs the notion of perfect graphs based on coloring. Let G be a k-uniform hypergraph. A coloring of a k-uniform hypergraph G is proper if it is a coloring of the (k − 1)-tuples with elements in V(G) in such a way that no edge of G is a monochromatic \(K_k^{k - 1}\). A k-uniform
-
Random colorings in manifolds Isr. J. Math. (IF 1.0) Pub Date : 2023-10-10 Chaim Even-Zohar, Joel Hass
We develop a general method for constructing random manifolds and sub-manifolds in arbitrary dimensions. The method is based on associating colors to the vertices of a triangulated manifold, as in recent work for curves in 3-dimensional space by Sheffield and Yadin (2014). We determine conditions on which submanifolds can arise, in terms of Stiefel–Whitney classes and other properties. We then consider
-
Spanning trees with few non-leaves Isr. J. Math. (IF 1.0) Pub Date : 2023-10-10 Noga Alon
Let f (n, k) denote the smallest number so that every connected graph with n vertices and minimum degree at least k contains a spanning tree in which the number of non-leaves is at most f (n, k). An early result of Linial and Sturtevant asserting that f (n, 3) = 3n/4 + O(1) and a related conjecture suggested by Linial led to a significant amount of work studying this function. It is known that for
-
Substructures in Latin squares Isr. J. Math. (IF 1.0) Pub Date : 2023-10-06 Matthew Kwan, Ashwin Sah, Mehtaab Sawhney, Michael Simkin
We prove several results about substructures in Latin squares. First, we explain how to adapt our recent work on high-girth Steiner triple systems to the setting of Latin squares, resolving a conjecture of Linial that there exist Latin squares with arbitrarily high girth. As a consequence, we see that the number of order-n Latin squares with no intercalate (i.e., no 2 × 2 Latin subsquare) is at least
-
On the d-dimensional algebraic connectivity of graphs Isr. J. Math. (IF 1.0) Pub Date : 2023-10-06 Alan Lew, Eran Nevo, Yuval Peled, Orit E. Raz
The d-dimensional algebraic connectivity ad(G) of a graph G = (V,E), introduced by Jordán and Tanigawa, is a quantitative measure of the d-dimensional rigidity of G that is defined in terms of the eigenvalues of stiffness matrices (which are analogues of the graph Laplacian) associated to mappings of the vertex set V into ℝd. Here, we analyze the d-dimensional algebraic connectivity of complete graphs
-
Connections between graphs and matrix spaces Isr. J. Math. (IF 1.0) Pub Date : 2023-10-06 Yinan Li, Youming Qiao, Avi Wigderson, Yuval Wigderson, Chuanqi Zhang
Given a bipartite graph G, the graphical matrix space \(\cal{S}_{G}\) consists of matrices whose non-zero entries can only be at those positions corresponding to edges in G. Tutte (J. London Math. Soc., 1947), Edmonds (J. Res. Nat. Bur. Standards Sect. B, 1967) and Lovász (FCT, 1979) observed connections between perfect matchings in G and full-rank matrices in \(\cal{S}_{G}\). Dieudonné (Arch. Math
-
Around the log-rank conjecture Isr. J. Math. (IF 1.0) Pub Date : 2023-10-06 Troy Lee, Adi Shraibman
The log-rank conjecture states that the communication complexity of a boolean matrix A is bounded by a polynomial in the log of the rank of A. Equivalently, it says that the chromatic number of a graph is bounded quasi-polynomially in the rank of its adjacency matrix. This old conjecture is well known among computer scientists and mathematicians, but despite extensive work it is still wide open. We
-
Spectral dimension, Euclidean embeddings, and the metric growth exponent Isr. J. Math. (IF 1.0) Pub Date : 2023-10-06 James R. Lee
For reversible random networks, we exhibit a relationship between the almost sure spectral dimension and the Euclidean growth exponent, which is the smallest asymptotic rate of volume growth over all embeddings of the network into a Hilbert space. Using metric embedding theory, it is then shown that the Euclidean growth exponent coincides with the metric growth exponent. This simplifies and generalizes