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Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals Ann. Comb. (IF 0.5) Pub Date : 2024-03-18 Hoi Ping Luk, Ho Man Cheung
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Some Results for Bipartition Difference Functions Ann. Comb. (IF 0.5) Pub Date : 2024-03-01 Bernard L. S. Lin, Xiaowei Lin
Inspired by a recent work of Kim, Kim and Lovejoy on two overpartition difference functions, we study some bipartition difference functions, four of which are related to Ramanujan’s identities recorded in his lost notebook. We show that they are always positive by elementary q-series transformations.
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Turán Problems for Oriented Graphs Ann. Comb. (IF 0.5) Pub Date : 2024-02-29
Abstract A classical Turán problem asks for the maximum possible number of edges in a graph of a given order that does not contain a particular graph H as a subgraph. It is well-known that the chromatic number of H is the graph parameter which describes the asymptotic behavior of this maximum. Here, we consider an analogous problem for oriented graphs, where compressibility plays the role of the chromatic
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Chainlink Polytopes and Ehrhart Equivalence Ann. Comb. (IF 0.5) Pub Date : 2024-02-06 Ezgi Kantarcı Oǧuz, Cem Yalım Özel, Mohan Ravichandran
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A Spin Analog of the Plethystic Murnaghan–Nakayama Rule Ann. Comb. (IF 0.5) Pub Date : 2024-02-06 Yue Cao, Naihuan Jing, Ning Liu
As a spin analog of the plethystic Murnaghan–Nakayama rule for Schur functions, the plethystic Murnaghan–Nakayama rule for Schur Q-functions is established with the help of the vertex operator realization. This generalizes both the Murnaghan–Nakayama rule and the Pieri rule for Schur Q-functions. A plethystic Murnaghan–Nakayama rule for Hall–Littlewood functions is also investigated.
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The Maximum Number of Cliques in Graphs with Bounded Odd Circumference Ann. Comb. (IF 0.5) Pub Date : 2024-01-24 Zequn Lv, Ervin Győri, Zhen He, Nika Salia, Chuanqi Xiao, Xiutao Zhu
In this work, we give the sharp upper bound for the number of cliques in graphs with bounded odd circumferences. This generalized Turán-type result is an extension of the celebrated Erdős and Gallai theorem and a strengthening of Luo’s recent result. The same bound for graphs with bounded even circumferences is a trivial application of the theorem of Li and Ning.
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A Unified Combinatorial Treatment for Three Classical Truncated Theta Series Ann. Comb. (IF 0.5) Pub Date : 2024-01-23 Andrew Y. Z. Wang, Ang Xiao
There has been a tremendous amount of research on the truncated theta series in the past decade. How can we understand them combinatorially? In this paper, we investigate the truncated theorems of three classical theta series of Euler and Gauss, and provide a unified combinatorial treatment. Meanwhile, we propose a possible and more direct approach to deal with these truncated theorems.
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A Succinct Proof of Defant and Kravitz’s Theorem on the Length of Hitomezashi Loops Ann. Comb. (IF 0.5) Pub Date : 2024-01-02 Qiuyu Ren, Shengtong Zhang
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Two Enriched Poset Polytopes Ann. Comb. (IF 0.5) Pub Date : 2023-12-22 Soichi Okada, Akiyoshi Tsuchiya
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An Asymptotic Lower Bound on the Number of Polyominoes Ann. Comb. (IF 0.5) Pub Date : 2023-12-21 Vuong Bui
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Approximate Sampling of Graphs with Near-P-Stable Degree Intervals Ann. Comb. (IF 0.5) Pub Date : 2023-12-21
Abstract The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current result about the well-studied switch Markov chain is that it is rapidly mixing on P-stable degree sequences (see DOI:10.1016/j.ejc.2021.103421). The switch
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Labeled Chip-Firing on Binary Trees with $$2^n-1$$ Chips Ann. Comb. (IF 0.5) Pub Date : 2023-12-15 Gregg Musiker, Son Nguyen
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The Hamilton Compression of Highly Symmetric Graphs Ann. Comb. (IF 0.5) Pub Date : 2023-12-13 Petr Gregor, Arturo Merino, Torsten Mütze
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The MacMahon q-Catalan is Convex Ann. Comb. (IF 0.5) Pub Date : 2023-12-12 Tewodros Amdeberhan, Stephan Wagner
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Techniques in Equivariant Ehrhart Theory Ann. Comb. (IF 0.5) Pub Date : 2023-11-21 Sophia Elia, Donghyun Kim, Mariel Supina
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Strongly Proper Connected Coloring of Graphs Ann. Comb. (IF 0.5) Pub Date : 2023-11-24 Michał Dębski, Jarosław Grytczuk, Paweł Naroski, Małgorzata Śleszyńska-Nowak
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Localised Graph Maclaurin Inequalities Ann. Comb. (IF 0.5) Pub Date : 2023-11-11 Lucas Aragão, Victor Souza
The Maclaurin inequalities for graphs are a broad generalisation of the classical theorems of Turán and Zykov. In a nutshell they provide an asymptotically sharp answer to the following question: what is the maximum number of cliques of size q in a graph with a given number of cliques of size s and a given clique number? We prove an extension of the graph Maclaurin inequalities with a weight function
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Complexity of Ice Quiver Mutation Equivalence Ann. Comb. (IF 0.5) Pub Date : 2023-11-04 David Soukup
We prove NP-hardness results for determining whether ice quivers are mutation equivalent to quivers with given properties, specifically, determining whether an ice quiver is mutation equivalent to an ice quiver with exactly k arrows between any two of its vertices is NP-hard. Also, determining whether an ice quiver is mutation equivalent to a quiver with no edges between frozen vertices is strongly
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Generalized Parking Function Polytopes Ann. Comb. (IF 0.5) Pub Date : 2023-11-06 Mitsuki Hanada, John Lentfer, Andrés R. Vindas-Meléndez
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Cyclic Shuffle-Compatibility Via Cyclic Shuffle Algebras Ann. Comb. (IF 0.5) Pub Date : 2023-10-24 Jinting Liang, Bruce E. Sagan, Yan Zhuang
A permutation statistic \({{\,\textrm{st}\,}}\) is said to be shuffle-compatible if the distribution of \({{\,\textrm{st}\,}}\) over the set of shuffles of two disjoint permutations \(\pi \) and \(\sigma \) depends only on \({{\,\textrm{st}\,}}\pi \), \({{\,\textrm{st}\,}}\sigma \), and the lengths of \(\pi \) and \(\sigma \). Shuffle-compatibility is implicit in Stanley’s early work on P-partitions
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Bargain Hunting in a Coxeter Group Ann. Comb. (IF 0.5) Pub Date : 2023-10-25 Joel Brewster Lewis, Bridget Eileen Tenner
Petersen and Tenner defined the depth statistic for Coxeter group elements which, in the symmetric group, can be described in terms of a cost function on transpositions. We generalize that cost function to the other classical (finite and affine) Weyl groups, letting the cost of an individual reflection t be the distance between the integers transposed by t in the combinatorial representation of the
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Positivity Properties for Spherical Functions of Maximal Young Subgroups Ann. Comb. (IF 0.5) Pub Date : 2023-10-25 R. M. Green
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Dyck Paths, Binary Words, and Grassmannian Permutations Avoiding an Increasing Pattern Ann. Comb. (IF 0.5) Pub Date : 2023-10-19 Krishna Menon, Anurag Singh
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On the Homotopy Type of the Iterated Clique Graphs of Low Degree Ann. Comb. (IF 0.5) Pub Date : 2023-10-10 Mauricio Islas-Gómez, Rafael Villarroel-Flores
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Combinatorics of Euclidean Spaces over Finite Fields Ann. Comb. (IF 0.5) Pub Date : 2023-09-20 Semin Yoo
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Some Consequences of the Valley Delta Conjectures Ann. Comb. (IF 0.5) Pub Date : 2023-09-11 Michele D’Adderio, Alessandro Iraci
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Combinatorics of Exterior Peaks on Pattern-Avoiding Symmetric Transversals Ann. Comb. (IF 0.5) Pub Date : 2023-09-15 Robin D. P. Zhou, Sherry H. F. Yan
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A Conjectured Formula for the Rational $$\varvec{q},\varvec{t}$$ -Catalan Polynomial Ann. Comb. (IF 0.5) Pub Date : 2023-09-07 Graham Hawkes
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On Distance-Balanced Generalized Petersen Graphs Ann. Comb. (IF 0.5) Pub Date : 2023-08-17 Gang Ma, Jianfeng Wang, Sandi Klavžar
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A Murnaghan–Nakayama Rule for Grothendieck Polynomials of Grassmannian Type Ann. Comb. (IF 0.5) Pub Date : 2023-07-25 Duc-Khanh Nguyen, Dang Tuan Hiep, Tran Ha Son, Do Le Hai Thuy
We consider the Grothendieck polynomials appearing in the K-theory of Grassmannians, which are analogs of Schur polynomials. This paper aims to establish a version of the Murnaghan–Nakayama rule for Grothendieck polynomials of the Grassmannian type. This rule allows us to express the product of a Grothendieck polynomial with a power-sum symmetric polynomial into a linear combination of other Grothendieck
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Combinatorial Properties of Three Classical Truncated Theta Series Theorems Ann. Comb. (IF 0.5) Pub Date : 2023-07-03 Andrew Y. Z. Wang, Ang Xiao
In this paper, we focus on the truncations of three classical theta series of Euler and Gauss, and analyze their combinatorial properties which play a key role in proving these truncated identities. Several interesting partition identities are established bijectively.
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On the Compatible Sets Expansion of the Tutte Polynomial Ann. Comb. (IF 0.5) Pub Date : 2023-06-30 Laura Pierson
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Asymptotics of Multivariate Sequences IV: Generating Functions with Poles on a Hyperplane Arrangement Ann. Comb. (IF 0.5) Pub Date : 2023-06-13 Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle
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The Space of Equidistant Phylogenetic Cactuses Ann. Comb. (IF 0.5) Pub Date : 2023-06-09 Katharina T. Huber, Vincent Moulton, Megan Owen, Andreas Spillner, Katherine St. John
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On Discrete Gradient Vector Fields and Laplacians of Simplicial Complexes Ann. Comb. (IF 0.5) Pub Date : 2023-05-30 Ivan Contreras, Andrew Tawfeek
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Folding Rotationally Symmetric Tableaux via Webs Ann. Comb. (IF 0.5) Pub Date : 2023-05-29 Kevin Purbhoo, Shelley Wu
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Partial Symmetries of Iterated Plethysms Ann. Comb. (IF 0.5) Pub Date : 2023-05-29 Álvaro Gutiérrez, Mercedes H. Rosas
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Long Twins in Random Words Ann. Comb. (IF 0.5) Pub Date : 2023-05-23 Andrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński
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On the Subdivision Algebra for the Polytope $$\mathcal {U}_{I,\overline{J}}$$ Ann. Comb. (IF 0.5) Pub Date : 2023-05-19 Matias von Bell, Martha Yip
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Refined Enumeration of $${{\varvec{k}}}$$ -plane Trees and $${\varvec{k}}$$ -noncrossing Trees Ann. Comb. (IF 0.5) Pub Date : 2023-05-10 Isaac Owino Okoth, Stephan Wagner
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The Rank of the Sandpile Group of Random Directed Bipartite Graphs Ann. Comb. (IF 0.5) Pub Date : 2023-04-28 Atal Bhargava, Jack DePascale, Jake Koenig
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On Promotion and Quasi-Tangled Labelings of Posets Ann. Comb. (IF 0.5) Pub Date : 2023-04-20 Eliot Hodges
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Arithmetic Properties of Certain t-Regular Partitions Ann. Comb. (IF 0.5) Pub Date : 2023-04-18 Rupam Barman, Ajit Singh, Gurinder Singh
For a positive integer \(t\ge 2\), let \(b_{t}(n)\) denote the number of t-regular partitions of a nonnegative integer n. Motivated by some recent conjectures of Keith and Zanello, we establish infinite families of congruences modulo 2 for \(b_9(n)\) and \(b_{19}(n)\). We prove some specific cases of two conjectures of Keith and Zanello on self-similarities of \(b_9(n)\) and \(b_{19}(n)\) modulo 2
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Bressoud–Subbarao Type Weighted Partition Identities for a Generalized Divisor Function Ann. Comb. (IF 0.5) Pub Date : 2023-04-17 Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni, Bibekananda Maji
In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a q-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao
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Congruence Modulo 4 for Andrews’ Even Parts Below Odd Parts Partition Function Ann. Comb. (IF 0.5) Pub Date : 2023-03-29 Dandan Chen, Rong Chen
We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of \(\overline{\mathcal{E}\mathcal{O}}(n)\) and further prove that \(\overline{\mathcal{E}\mathcal{O}}(n)\equiv 0\pmod 4\) for almost all n. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.
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Embedding Dimensions of Simplicial Complexes on Few Vertices Ann. Comb. (IF 0.5) Pub Date : 2023-03-28 Florian Frick, Mirabel Hu, Verity Scheel, Steven Simon
We provide a simple characterization of simplicial complexes on few vertices that embed into the d-sphere. Namely, a simplicial complex on \(d+3\) vertices embeds into the d-sphere if and only if its non-faces do not form an intersecting family. As immediate consequences, we recover the classical van Kampen–Flores theorem and provide a topological extension of the Erdős–Ko–Rado theorem. By analogy
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Strict Log-Subadditivity for Overpartition Rank Ann. Comb. (IF 0.5) Pub Date : 2023-03-24 Helen W. J. Zhang, Ying Zhong
Bessenrodt and Ono initially found the strict log-subadditivity of partition function p(n), that is, \(p(a+b)< p(a)p(b)\) for \(a,b>1\) and \(a+b>9\). Many other important partition statistics are proved to enjoy similar properties. Lovejoy introduced the overpartition rank as an analog of Dyson’s rank for partitions from the q-series perspective. Let \({\overline{N}}(a,c,n)\) denote the number of
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Dominance Regions for Rank Two Cluster Algebras Ann. Comb. (IF 0.5) Pub Date : 2023-03-20 Dylan Rupel, Salvatore Stella
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Berkovich–Uncu Type Partition Inequalities Concerning Impermissible Sets and Perfect Power Frequencies Ann. Comb. (IF 0.5) Pub Date : 2023-03-16 Damanvir Singh Binner, Neha Gupta, Manoj Upreti
Recently, Rattan and the first author (Ann. Comb. 25 (2021) 697–728) proved a conjectured inequality of Berkovich and Uncu (Ann. Comb. 23 (2019) 263–284) concerning partitions with an impermissible part. In this article, we generalize this inequality upon considering t impermissible parts. We compare these with partitions whose certain parts appear with a frequency which is a perfect \(t^{th}\) power
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Identifying Young Diagrams Among Residue Multisets Ann. Comb. (IF 0.5) Pub Date : 2023-03-06 Salim Rostam
To any Young diagram we can associate the multiset of residues of all its nodes. This paper is concerned with the inverse problem: given a multiset of elements of \(\mathbb {Z}/e\mathbb {Z}\), does it comes from a Young diagram? We give a full solution in level one and a partial answer in higher levels for Young multidiagrams, using Fayers’s notions of core block and weight of a multipartition. We
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A Non-aligning Variant of Generalized Turán Problems Ann. Comb. (IF 0.5) Pub Date : 2023-02-25 Dániel Gerbner
In the so-called generalized Turán problems we study the largest number of copies of H in an n-vertex F-free graph G. Here we introduce a variant, where F is not forbidden, but we restrict how copies of H and F can be placed in G. More precisely, given an integer n and graphs H and F, what is the largest number of copies of H in an n-vertex graph such that the vertex set of that copy does not contain
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Lattice Paths and Negatively Indexed Weight-Dependent Binomial Coefficients Ann. Comb. (IF 0.5) Pub Date : 2023-02-21 Josef Küstner, Michael J. Schlosser, Meesue Yoo
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Coloring Bipartite Graphs with Semi-small List Size Ann. Comb. (IF 0.5) Pub Date : 2023-01-29 Daniel G. Zhu
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Factorisation of the Complete Bipartite Graph into Spanning Semiregular Factors Ann. Comb. (IF 0.5) Pub Date : 2023-01-29 Mahdieh Hasheminezhad, Brendan D. McKay
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Lagrangian-Perfect Hypergraphs Ann. Comb. (IF 0.5) Pub Date : 2023-01-06 Zilong Yan, Yuejian Peng
Hypergraph Lagrangian function has been a helpful tool in several celebrated results in extremal combinatorics. Let G be an r-uniform graph on [n] and let \({\textbf{x}}=(x_1,\ldots ,x_n) \in [0,\infty )^n.\) The graph Lagrangian function is defined to be \(\lambda (G,{\textbf{x}})=\sum _{e \in E(G)}\prod _{i\in e}x_{i}.\) The graph Lagrangian is defined as \(\lambda (G)=\max \{\lambda (G, {\textbf{x}}):
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Extremal $$\varvec{\{ p, q \}}$$ -Animals Ann. Comb. (IF 0.5) Pub Date : 2023-01-06 Greg Malen, Érika Roldán, Rosemberg Toalá-Enríquez
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On Antipodes of Immaculate Functions Ann. Comb. (IF 0.5) Pub Date : 2022-12-30 John Maxwell Campbell
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Boolean Complexes of Involutions Ann. Comb. (IF 0.5) Pub Date : 2022-12-28 Axel Hultman, Vincent Umutabazi
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Equivariant Euler Characteristics of Subgroup Complexes of Symmetric Groups Ann. Comb. (IF 0.5) Pub Date : 2022-12-17 Zhipeng Duan
Equivariant Euler characteristics are important numerical homotopy invariants for objects with group actions. They have deep connections with many other areas like modular representation theory and chromatic homotopy theory. They are also computable, especially for combinatorial objects like partition posets, buildings associated with finite groups of Lie types, etc. In this article, we make new contributions
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The Merino–Welsh Conjecture for Split Matroids Ann. Comb. (IF 0.5) Pub Date : 2022-12-17 Luis Ferroni, Benjamin Schröter