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  • On generalized Erdős–Ginzburg–Ziv constants for Z2d
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-31
    Alexander Sidorenko

    Let G be a finite abelian group, and r be a multiple of its exponent. The generalized Erdős–Ginzburg–Ziv constant sr(G) is the smallest integer s such that every sequence of length s over G has a zero-sum subsequence of length r. We find exact values of s2m(Z2d) for d≤2m+1. Connections to linear binary codes of maximal length and codes without a forbidden weight are discussed.

    更新日期:2020-03-31
  • Walks in the quarter plane: Genus zero case
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-31
    Thomas Dreyfus; Charlotte Hardouin; Julien Roques; Michael F. Singer

    We use Galois theory of difference equations to study the nature of the generating series of (weighted) walks in the quarter plane with genus zero kernel curve. Using this approach, we prove that the generating series do not satisfy any nontrivial (possibly nonlinear) algebraic differential equation with rational coefficients.

    更新日期:2020-03-31
  • Symmetric multisets of permutations
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-27
    Jonathan S. Bloom

    The following long-standing problem in combinatorics was first posed in 1993 by Gessel and Reutenauer [5]. For which multisubsets B of the symmetric group Sn is the quasisymmetric functionQ(B)=∑π∈BFDes(π),n a symmetric function? Here Des(π) is the descent set of π and FDes(π),n is Gessel's fundamental basis for the vector space of quasisymmetric functions. The purpose of this paper is to provide a

    更新日期:2020-03-27
  • Bijective proofs of skew Schur polynomial factorizations
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-26
    Arvind Ayyer; Ilse Fischer

    In a recent paper, Ayyer and Behrend present for a wide class of partitions factorizations of Schur polynomials with an even number of variables where half of the variables are the reciprocals of the others into symplectic and/or orthogonal group characters, thereby generalizing results of Ciucu and Krattenthaler for rectangular shapes. Their proofs proceed by manipulations of determinants underlying

    更新日期:2020-03-27
  • Partitioning the vertices of a torus into isomorphic subgraphs
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-26
    Marthe Bonamy; Natasha Morrison; Alex Scott

    Let H be an induced subgraph of the torus Ckm. We show that when k≥3 is even and |V(H)| divides some power of k, then for sufficiently large n the torus Ckn has a perfect vertex-packing with induced copies of H. On the other hand, disproving a conjecture of Gruslys, we show that when k is odd and not a prime power, then there exists H such that |V(H)| divides some power of k, but there is no n such

    更新日期:2020-03-27
  • Catalan intervals and uniquely sorted permutations
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-20
    Colin Defant

    For each positive integer k, we consider five well-studied posets defined on the set of Dyck paths of semilength k. We prove that uniquely sorted permutations avoiding various patterns are equinumerous with intervals in these posets. While most of our proofs are bijective, some use generating trees and generating functions. We end with several conjectures.

    更新日期:2020-03-21
  • The partition rank of a tensor and k-right corners in Fqn
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-17
    Eric Naslund

    Following the breakthrough of Croot, Lev, and Pach [4], Tao [10] introduced a symmetrized version of their argument, which is now known as the slice rank method. In this paper, we introduce a more general version of the slice rank of a tensor, which we call the Partition Rank. This allows us to extend the slice rank method to problems that require the variables to be distinct. Using the partition rank

    更新日期:2020-03-19
  • Exponential bounds for the Erdős-Ginzburg-Ziv constant
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-17
    Eric Naslund

    The Erdős-Ginzburg-Ziv constant of a finite abelian group G, denoted s(G), is the smallest k∈N such that any sequence of elements of G of length k contains a zero-sum subsequence of length exp⁡(G). In this paper, we use the partition rank from [14], which generalizes the slice rank, to prove that for any odd prime p,s(Fpn)≤(p−1)2p(J(p)⋅p)n where 0.84143, this is the

    更新日期:2020-03-19
  • Bi-pruned Hurwitz numbers
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-13
    Marvin Anas Hahn

    Hurwitz numbers enumerate ramified coverings of the Riemann sphere with fixed ramification data. Certain kinds of ramification data are of particular interest, such as double Hurwitz numbers, which count covers with fixed arbitrary ramification over 0 and ∞ and simple ramification over b points, where b is given by the Riemann-Hurwitz formula. In this work, we introduce the notion of bi-pruned double

    更新日期:2020-03-16
  • On k-connected-homogeneous graphs
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-09
    Alice Devillers; Joanna B. Fawcett; Cheryl E. Praeger; Jin-Xin Zhou

    A graph Γ is k-connected-homogeneous (k-CH) if k is a positive integer and any isomorphism between connected induced subgraphs of order at most k extends to an automorphism of Γ, and connected-homogeneous (CH) if this property holds for all k. Locally finite, locally connected graphs often fail to be 4-CH because of a combinatorial obstruction called the unique x property; we prove that this property

    更新日期:2020-03-09
  • Vector parking functions with periodic boundaries and rational parking functions
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-02
    Yue Cai; Catherine H. Yan

    Vector parking functions are sequences of non-negative integers whose order statistics are bounded by a given integer sequence u=(u0,u1,u2,…). Using the theory of fractional power series and an analog of Newton-Puiseux Theorem, we derive the exponential generating function for the number of u-parking functions when u is periodic. Our method is to convert an Appell relation of Gončarov polynomials to

    更新日期:2020-03-03
  • Linear representations of finite geometries and associated LDPC codes
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-03-02
    Peter Sin; Julien Sorci; Qing Xiang

    The linear representation of a subset of a finite projective space is an incidence system of affine points and lines determined by the subset. In this paper we use character theory to show that the rank of the incidence matrix has a direct geometric interpretation in terms of certain hyperplanes. We consider the LDPC codes defined by taking the incidence matrix and its transpose as parity-check matrices

    更新日期:2020-03-03
  • A superlinear lower bound on the number of 5-holes
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-27
    Oswin Aichholzer; Martin Balko; Thomas Hackl; Jan Kynčl; Irene Parada; Manfred Scheucher; Pavel Valtr; Birgit Vogtenhuber

    Let P be a finite set of points in the plane in general position, that is, no three points of P are on a common line. We say that a set H of five points from P is a 5-hole in P if H is the vertex set of a convex 5-gon containing no other points of P. For a positive integer n, let h5(n) be the minimum number of 5-holes among all sets of n points in the plane in general position. Despite many efforts

    更新日期:2020-02-28
  • Stack sorting with restricted stacks
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-21
    Giulio Cerbai; Anders Claesson; Luca Ferrari

    The (classical) problem of characterizing and enumerating permutations that can be sorted using two stacks connected in series is still largely open. In the present paper we address a related problem, in which we impose restrictions both on the procedure and on the stacks. More precisely, we consider a greedy algorithm where we perform the rightmost legal operation. Moreover, the first stack is required

    更新日期:2020-02-21
  • A symplectic refinement of shifted Hecke insertion
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-21
    Eric Marberg

    Buch, Kresch, Shimozono, Tamvakis, and Yong defined Hecke insertion to formulate a combinatorial rule for the expansion of the stable Grothendieck polynomials Gπ indexed by permutations in the basis of stable Grothendieck polynomials Gλ indexed by partitions. Patrias and Pylyavskyy introduced a shifted analogue of Hecke insertion whose natural domain is the set of maximal chains in a weak order on

    更新日期:2020-02-21
  • Recognizing sets of generators in finite polar spaces
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-12
    Stefaan De Winter; Jeroen Schillewaert

    We characterize non-singular polar spaces embedded in non-singular polar spaces of the same rank using subsets of generators satisfying a natural intersection condition. By [7] and [8] this result has applications to the theory of Cameron-Liebler sets. In fact, our result is a significant improvement of the main result in [7].

    更新日期:2020-02-20
  • Divergent permutations
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-12
    Emanuela Fachini; János Körner

    Two permutations of the natural numbers diverge if the absolute value of the difference of their elements in the same position goes to infinity. We show that there exists an infinite number of pairwise divergent permutations of the naturals. We relate this result to more general questions about the permutation capacity of infinite graphs.

    更新日期:2020-02-20
  • Characterization of queer supercrystals
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-14
    Maria Gillespie; Graham Hawkes; Wencin Poh; Anne Schilling

    We provide a characterization of the crystal bases for the quantum queer superalgebra recently introduced by Grantcharov et al. This characterization is a combination of local queer axioms generalizing Stembridge's local axioms for crystal bases for simply-laced root systems, which were recently introduced by Assaf and Oguz, with further axioms and a new graph G characterizing the relations of the

    更新日期:2020-02-20
  • Degenerate Turán densities of sparse hypergraphs
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-13
    Chong Shangguan; Itzhak Tamo

    For fixed integers r>k≥2,e≥3, let fr(n,er−(e−1)k,e) be the maximum number of edges in an r-uniform hypergraph in which the union of any e distinct edges contains at least er−(e−1)k+1 vertices. A classical result of Brown, Erdős and Sós in 1973 showed that fr(n,er−(e−1)k,e)=Θ(nk). The degenerate Turán density is defined to be the limit (if it exists)π(r,k,e):=limn→∞⁡fr(n,er−(e−1)k,e)nk. Extending a

    更新日期:2020-02-20
  • On the Cheeger constant for distance-regular graphs
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-13
    Zhi Qiao; Jack H. Koolen; Greg Markowsky

    The Cheeger constant of a graph is the smallest possible ratio between the size of a subgraph and the size of its boundary. It is well known that this constant must be at least λ12, where λ1 is the smallest positive eigenvalue of the Laplacian matrix. The subject of this paper is a conjecture of the authors that for distance-regular graphs the Cheeger constant is at most λ1. In particular, we prove

    更新日期:2020-02-20
  • Families of lattice polytopes of mixed degree one
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-17
    Gabriele Balletti; Christopher Borger

    It has been shown by Soprunov that the normalized mixed volume (minus one) of an n-tuple of n-dimensional lattice polytopes is a lower bound for the number of interior lattice points in the Minkowski sum of the polytopes. He defined n-tuples of mixed degree at most one to be exactly those for which this lower bound is attained with equality, and posed the problem of a classification of such tuples

    更新日期:2020-02-20
  • A combinatorial approach for discrete car parking on random labelled trees
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-14
    Alois Panholzer

    We consider two analogues of a discrete version of the famous car parking problem of Rényi for trees, which are also known under the term random sequential adsorption. For both models, the blocking model, where cars arrive sequentially at the nodes and only park if the site and all neighbouring nodes are free, and the dimer model, where cars arrive sequentially at the edges and only park if both endnodes

    更新日期:2020-02-20
  • Recursions for rational q,t-Catalan numbers
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-17
    Eugene Gorsky; Mikhail Mazin; Monica Vazirani

    We give a simple recursion labeled by binary sequences which computes rational q,t-Catalan power series, both in relatively prime and non relatively prime cases. It is inspired by, but not identical to recursions due to B. Elias, M. Hogancamp, and A. Mellit, obtained in their study of link homology. We also compare our recursion with the Hogancamp-Mellit's recursion and verify a connection between

    更新日期:2020-02-20
  • The negative tetrahedron and the first infinite family of connected digraphs that are strongly determined by the Hermitian spectrum
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-02-20
    Pepijn Wissing; Edwin R. van Dam

    Thus far, digraphs that are uniquely determined by their Hermitian spectra have proven elusive. Instead, researchers have turned to spectral determination of classes of switching equivalent digraphs, rather than individual digraphs. In the present paper, we consider the traditional notion: a digraph (or mixed graph) is said to be strongly determined by its Hermitian spectrum (abbreviated SHDS) if it

    更新日期:2020-02-20
  • Binomial Eulerian polynomials for colored permutations
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-27
    Christos A. Athanasiadis

    Binomial Eulerian polynomials first appeared in work of Postnikov, Reiner and Williams on the face enumeration of generalized permutohedra. They are γ-positive (in particular, palindromic and unimodal) polynomials which can be interpreted as h-polynomials of certain flag simplicial polytopes and which admit interesting Schur γ-positive symmetric function generalizations. This paper introduces analogues

    更新日期:2020-01-27
  • A combinatorial formula for the Ehrhart h⁎-vector of the hypersimplex
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-27
    Donghyun Kim

    We give a combinatorial formula for the Ehrhart h⁎-vector of the hypersimplex. In particular, we show that hd⁎(Δk,n) is the number of hypersimplicial decorated ordered set partitions of type (k,n) with winding number d, thereby proving a conjecture of N. Early. We do this by proving a more general conjecture of N. Early on the Ehrhart h⁎-vector of a generic cross-section of a hypercube.

    更新日期:2020-01-27
  • Total non-negativity of some combinatorial matrices
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-23
    David Galvin; Adrian Pacurar

    Many combinatorial matrices — such as those of binomial coefficients, Stirling numbers of both kinds, and Lah numbers — are known to be totally non-negative, meaning that all minors (determinants of square submatrices) are non-negative. The examples noted above can be placed in a common framework: for each one there is a non-decreasing sequence (a1,a2,…), and a sequence (e1,e2,…), such that the (m

    更新日期:2020-01-24
  • Chromatic numbers of Kneser-type graphs
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-23
    Dmitriy Zakharov

    Let G(n,r,s) be a graph whose vertices are all r-element subsets of an n-element set, in which two vertices are adjacent if they intersect in exactly s elements. In this paper we study chromatic numbers of G(n,r,s) with r,s being fixed constants and n tending to infinity. Using a recent result of Keevash on existence of designs we deduce an inequality χ(G(n,r,s))⩽(1+o(1))nr−s(r−s−1)!(2r−2s−1)! for

    更新日期:2020-01-24
  • Rainbow factors in hypergraphs
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-23
    Matthew Coulson; Peter Keevash; Guillem Perarnau; Liana Yepremyan

    For any r-graph H, we consider the problem of finding a rainbow H-factor in an r-graph G with large minimum ℓ-degree and an edge-colouring that is suitably bounded. We show that the asymptotic degree threshold is the same as that for finding an H-factor.

    更新日期:2020-01-24
  • e-Positivity of vertical strip LLT polynomials
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-22
    Michele D'Adderio

    In this article we prove the e-positivity of Gν[X;q+1] when Gν[X;q] is a vertical strip LLT polynomial. This property has been conjectured in [2] and [7], and it implies several e-positivities conjectured in those references and in [3]. We make use of a result of Carlsson and Mellit [5] that shows that a vertical strip LLT polynomial can be obtained by applying certain compositions of operators of

    更新日期:2020-01-23
  • Counting 3-stack-sortable permutations
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-21
    Colin Defant

    We prove a “decomposition lemma” that allows us to count preimages of certain sets of permutations under West's stack-sorting map s. As a first application, we give a new proof of Zeilberger's formula for the number W2(n) of 2-stack-sortable permutations in Sn. Our proof generalizes, allowing us to find an algebraic equation satisfied by the generating function that counts 2-stack-sortable permutations

    更新日期:2020-01-22
  • The Steep-Bounce zeta map in Parabolic Cataland
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-20
    Cesar Ceballos; Wenjie Fang; Henri Mühle

    As a classical object, the Tamari lattice has many generalizations, including ν-Tamari lattices and parabolic Tamari lattices. In this article, we unify these generalizations in a bijective fashion. We first prove that parabolic Tamari lattices are isomorphic to ν-Tamari lattices for bounce paths ν. We then introduce a new combinatorial object called “left-aligned colorable tree”, and show that it

    更新日期:2020-01-21
  • Elementary moves on lattice polytopes
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-16
    Julien David; Lionel Pournin; Rado Rakotonarivo

    We introduce a graph structure on the set of Euclidean polytopes. The vertices of this graph are the d-dimensional polytopes contained in Rd and its edges connect any two polytopes that can be obtained from one another by either inserting or deleting a vertex, while keeping their vertex sets otherwise unaffected. We prove several results on the connectivity of this graph, and on a number of its subgraphs

    更新日期:2020-01-21
  • The EKR property for flag pure simplicial complexes without boundary
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-14
    Jorge Alberto Olarte; Francisco Santos; Jonathan Spreer; Christian Stump

    We prove that the family of facets of a pure simplicial complex C of dimension up to three satisfies the Erdős-Ko-Rado property whenever C is flag and has no boundary ridges. We conjecture the same to be true in arbitrary dimension and give evidence for this conjecture. Our motivation is that complexes with these two properties include flag pseudo-manifolds and cluster complexes.

    更新日期:2020-01-15
  • Chordality, d-collapsibility, and componentwise linear ideals
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-14
    Mina Bigdeli; Sara Faridi

    Using the concept of d-collapsibility from combinatorial topology, we define chordal simplicial complexes and show that their Stanley-Reisner ideals are componentwise linear. Our construction is inspired by and an extension of “chordal clutters” which was defined by Bigdeli, Yazdan Pour and Zaare-Nahandi in 2017, and characterizes Betti tables of all ideals with a linear resolution in a polynomial

    更新日期:2020-01-15
  • On the ℓ4:ℓ2 ratio of functions with restricted Fourier support
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-14
    Naomi Kirshner; Alex Samorodnitsky

    Given a subset A⊆{0,1}n, let μ(A) be the maximal ratio between ℓ4 and ℓ2 norms of a function whose Fourier support is a subset of A.1 We make some simple observations about the connections between μ(A) and the additive properties of A on one hand, and between μ(A) and the uncertainty principle for A on the other hand. One application obtained by combining these observations with results in additive

    更新日期:2020-01-15
  • On the interplay between additive and multiplicative largeness and its combinatorial applications
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-13
    Vitaly Bergelson; Daniel Glasscock

    Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of N and in more general ring-theoretic structures. We show that multiplicative largeness begets additive largeness in three ways and give a collection of examples demonstrating the optimality of these results. We also give

    更新日期:2020-01-14
  • Toeplitz minors and specializations of skew Schur polynomials
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-06
    David García-García; Miguel Tierz

    We express minors of Toeplitz matrices of finite and large dimension in terms of symmetric functions. Comparing the resulting expressions with the inverses of some Toeplitz matrices, we obtain explicit formulas for a Selberg-Morris integral and for specializations of certain skew Schur polynomials.

    更新日期:2020-01-07
  • 3D positive lattice walks and spherical triangles
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-06
    B. Bogosel; V. Perrollaz; K. Raschel; A. Trotignon

    In this paper we explore the asymptotic enumeration of three-dimensional excursions confined to the positive octant. As shown in [29], both the exponential growth and the critical exponent admit universal formulas, respectively in terms of the inventory of the step set and of the principal Dirichlet eigenvalue of a certain spherical triangle, itself being characterized by the steps of the model. We

    更新日期:2020-01-07
  • New necessary conditions on (negative) Latin square type partial difference sets in abelian groups
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-07
    Zeying Wang

    Partial difference sets (for short, PDSs) with parameters (n2, r(n−ϵ), ϵn+r2−3ϵr, r2−ϵr) are called Latin square type (respectively negative Latin square type) PDSs if ϵ=1 (respectively ϵ=−1). In this paper, we will give restrictions on the parameter r of a (negative) Latin square type partial difference set in an abelian group of non-prime power order a2b2, where gcd⁡(a,b)=1, a>1, and b is an odd

    更新日期:2020-01-07
  • A generalized Eulerian triangle from staircase tableaux and tree-like tableaux
    J. Comb. Theory A (IF 0.958) Pub Date : 2020-01-07
    Bao-Xuan Zhu

    Motivated by the classical Eulerian triangle and triangular arrays from staircase tableaux and tree-like tableaux, we study a generalized Eulerian array [Tn,k]n,k≥0, which satisfies the recurrence relation:Tn,k=λ(a1k+a2)Tn−1,k+[(b1−da1)n−(b1−2da1)k+b2−d(a1−a2)]Tn−1,k−1+d(b1−da1)λ(n−k+1)Tn−1,k−2, where T0,0=1 and Tn,k=0 unless 0≤k≤n. We derive some properties of [Tn,k]n,k≥0, including the explicit formulae

    更新日期:2020-01-07
  • New code upper bounds for the folded n-cube
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-26
    Lihang Hou; Bo Hou; Suogang Gao; Wei-Hsuan Yu

    Let □n denote the folded n-cube and let A(□n,d) denote the maximum size of a code in □n with minimum distance at least d. We give an upper bound on A(□n,d) based on block-diagonalizing the Terwilliger algebra of □n and on semidefinite programming. The technique of this paper is an extension of the approach taken by A. Schrijver [11] on the study of upper bounds for binary codes.

    更新日期:2020-01-04
  • Erdős-Ko-Rado theorems for set partitions with certain block size
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-12
    Cheng Yeaw Ku; Kok Bin Wong

    In this paper, we prove Erdős-Ko-Rado type results for (a) family of set partitions where the size of each block is a multiple of k; and (b) family of set partitions with minimum block size k.

    更新日期:2020-01-04
  • State transfer in strongly regular graphs with an edge perturbation
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-12
    Chris Godsil; Krystal Guo; Mark Kempton; Gabor Lippner; Florentin Münch

    Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is understood to be a rare and interesting phenomenon. We consider a perturbation on an edge uv of a graph where we add a weight β to the edge and a loop of weight γ to each

    更新日期:2020-01-04
  • Pattern groups and a poset based Hopf monoid
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-27
    Farid Aliniaeifard; Nathaniel Thiem

    The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two canonical bases, one of which was completely new in terms of symmetric functions. This paper simultaneously generalizes this Hopf structure by considering a larger class

    更新日期:2020-01-04
  • The generating function of planar Eulerian orientations
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-16
    Mireille Bousquet-Mélou; Andrew Elvey Price

    The enumeration of planar maps equipped with an Eulerian orientation has attracted attention in both combinatorics and theoretical physics since at least 2000. The case of 4-valent maps is particularly interesting: these orientations are in bijection with properly 3-coloured quadrangulations, while in physics they correspond to configurations of the ice model. We solve both problems – namely the enumeration

    更新日期:2020-01-04
  • Asymptotic enumeration of compacted binary trees of bounded right height
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-30
    Antoine Genitrini; Bernhard Gittenberger; Manuel Kauers; Michael Wallner

    A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special class of directed acyclic graphs. We are interested in the asymptotic number of compacted trees of given size, where the size of a compacted tree is given by the

    更新日期:2020-01-04
  • Winding of simple walks on the square lattice
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-31
    Timothy Budd

    A method is described to count simple diagonal walks on Z2 with a fixed starting point and endpoint on one of the axes and a fixed winding angle around the origin. The method involves the decomposition of such walks into smaller pieces, the generating functions of which are encoded in a commuting set of Hilbert space operators. The general enumeration problem is then solved by obtaining an explicit

    更新日期:2020-01-04
  • Vertex-isoperimetric stability in the hypercube
    J. Comb. Theory A (IF 0.958) Pub Date : 2019-12-31
    Michał Przykucki; Alexander Roberts

    Harper's Theorem states that, in a hypercube, among all sets of a given fixed size the Hamming balls have minimal closed neighbourhoods. In this paper we prove a stability-like result for Harper's Theorem: if the closed neighbourhood of a set is close to minimal in the hypercube, then the set must be very close to a Hamming ball around some vertex.

    更新日期:2020-01-04
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