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Annals of Combinatorics最新文献

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Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals 有理角度和全等四边形对球面的倾斜
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-03-18 DOI: 10.1007/s00026-023-00685-9
Hoi Ping Luk, Ho Man Cheung
{"title":"Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals","authors":"Hoi Ping Luk,&nbsp;Ho Man Cheung","doi":"10.1007/s00026-023-00685-9","DOIUrl":"10.1007/s00026-023-00685-9","url":null,"abstract":"<div><p>We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination <span>(a^3b)</span>). Parallel to a complete classification by Cheung, Luk, and Yan, the method implemented here is more systematic and applicable to other related tiling problems. We also provide detailed geometric data for the tilings.\u0000</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 2","pages":"485 - 527"},"PeriodicalIF":0.6,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00685-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140146624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Results for Bipartition Difference Functions 双分区差分函数的一些结果
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-03-01 DOI: 10.1007/s00026-024-00688-0
Bernard L. S. Lin, Xiaowei Lin
{"title":"Some Results for Bipartition Difference Functions","authors":"Bernard L. S. Lin,&nbsp;Xiaowei Lin","doi":"10.1007/s00026-024-00688-0","DOIUrl":"10.1007/s00026-024-00688-0","url":null,"abstract":"<div><p>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 <i>q</i>-series transformations.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1347 - 1361"},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Turán Problems for Oriented Graphs 定向图的图兰问题
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-02-29 DOI: 10.1007/s00026-024-00687-1
Andrzej Grzesik, Justyna Jaworska, Bartłomiej Kielak, Aliaksandra Novik, Tomasz Ślusarczyk
{"title":"Turán Problems for Oriented Graphs","authors":"Andrzej Grzesik,&nbsp;Justyna Jaworska,&nbsp;Bartłomiej Kielak,&nbsp;Aliaksandra Novik,&nbsp;Tomasz Ślusarczyk","doi":"10.1007/s00026-024-00687-1","DOIUrl":"10.1007/s00026-024-00687-1","url":null,"abstract":"<div><p>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 <i>H</i> as a subgraph. It is well-known that the chromatic number of <i>H</i> 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 number. Since any oriented graph having a directed cycle is not contained in any transitive tournament, it makes sense to consider only acyclic oriented graphs as forbidden subgraphs. We provide basic properties of the compressibility, show that the compressibility of acyclic oriented graphs with out-degree at most 2 is polynomial with respect to the maximum length of a directed path, and that the same holds for a larger out-degree bound if the Erdős–Hajnal conjecture is true. Additionally, generalizing previous results on powers of paths and arbitrary orientations of cycles, we determine the compressibility of acyclic oriented graphs with restricted distances of vertices to sinks and sources.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1303 - 1322"},"PeriodicalIF":0.6,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Spin Analog of the Plethystic Murnaghan–Nakayama Rule 褶皱型穆纳汉-中山规则的自旋类似物
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-02-06 DOI: 10.1007/s00026-023-00686-8
Yue Cao, Naihuan Jing, Ning Liu
{"title":"A Spin Analog of the Plethystic Murnaghan–Nakayama Rule","authors":"Yue Cao,&nbsp;Naihuan Jing,&nbsp;Ning Liu","doi":"10.1007/s00026-023-00686-8","DOIUrl":"10.1007/s00026-023-00686-8","url":null,"abstract":"<div><p>As a spin analog of the plethystic Murnaghan–Nakayama rule for Schur functions, the plethystic Murnaghan–Nakayama rule for Schur <i>Q</i>-functions is established with the help of the vertex operator realization. This generalizes both the Murnaghan–Nakayama rule and the Pieri rule for Schur <i>Q</i>-functions. A plethystic Murnaghan–Nakayama rule for Hall–Littlewood functions is also investigated.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 2","pages":"655 - 679"},"PeriodicalIF":0.6,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chainlink Polytopes and Ehrhart Equivalence 链锁多面体和艾哈特等价性
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-02-06 DOI: 10.1007/s00026-023-00683-x
Ezgi Kantarcı Oǧuz, Cem Yalım Özel, Mohan Ravichandran
{"title":"Chainlink Polytopes and Ehrhart Equivalence","authors":"Ezgi Kantarcı Oǧuz,&nbsp;Cem Yalım Özel,&nbsp;Mohan Ravichandran","doi":"10.1007/s00026-023-00683-x","DOIUrl":"10.1007/s00026-023-00683-x","url":null,"abstract":"<div><p>We introduce a class of polytopes that we call chainlink polytopes and show that they allow us to construct infinite families of pairs of non-isomorphic rational polytopes with the same Ehrhart quasipolynomial. Our construction is based on circular fence posets, a recently introduced class of posets, which admit a non-obvious and nontrivial symmetry in their rank sequences. We show that this symmetry can be lifted to the level of polyhedral models (which we call chainlink polytopes) for these posets. Along the way, we introduce the related class of chainlink posets and show that they exhibit analogous nontrivial symmetry properties. We further prove an outstanding conjecture on the unimodality of rank polynomials of circular fence posets.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1141 - 1166"},"PeriodicalIF":0.6,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Maximum Number of Cliques in Graphs with Bounded Odd Circumference 有界奇数圆周图中的最大聚类数
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-01-24 DOI: 10.1007/s00026-023-00682-y
Zequn Lv, Ervin Győri, Zhen He, Nika Salia, Chuanqi Xiao, Xiutao Zhu
{"title":"The Maximum Number of Cliques in Graphs with Bounded Odd Circumference","authors":"Zequn Lv,&nbsp;Ervin Győri,&nbsp;Zhen He,&nbsp;Nika Salia,&nbsp;Chuanqi Xiao,&nbsp;Xiutao Zhu","doi":"10.1007/s00026-023-00682-y","DOIUrl":"10.1007/s00026-023-00682-y","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1119 - 1125"},"PeriodicalIF":0.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00682-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Unified Combinatorial Treatment for Three Classical Truncated Theta Series 三种经典截断θ数列的统一组合处理方法
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-01-23 DOI: 10.1007/s00026-023-00684-w
Andrew Y. Z. Wang, Ang Xiao
{"title":"A Unified Combinatorial Treatment for Three Classical Truncated Theta Series","authors":"Andrew Y. Z. Wang,&nbsp;Ang Xiao","doi":"10.1007/s00026-023-00684-w","DOIUrl":"10.1007/s00026-023-00684-w","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 1","pages":"47 - 63"},"PeriodicalIF":0.6,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139558141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Succinct Proof of Defant and Kravitz’s Theorem on the Length of Hitomezashi Loops 德凡特和克拉维茨关于人字形环路长度定理的简明证明
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-01-02 DOI: 10.1007/s00026-023-00681-z
Qiuyu Ren, Shengtong Zhang
{"title":"A Succinct Proof of Defant and Kravitz’s Theorem on the Length of Hitomezashi Loops","authors":"Qiuyu Ren,&nbsp;Shengtong Zhang","doi":"10.1007/s00026-023-00681-z","DOIUrl":"10.1007/s00026-023-00681-z","url":null,"abstract":"<div><p>We provide a much shorter proof of Defant and Kravitz’s theorem that the length of Hitomezashi loops is congruent to 4 modulo 8. Our novel idea is to consider the length module 8 for Hitomezashi paths that take an excursion in a half-plane region.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 1","pages":"117 - 122"},"PeriodicalIF":0.6,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two Enriched Poset Polytopes 两个丰富的 Poset 多面体
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2023-12-22 DOI: 10.1007/s00026-023-00679-7
Soichi Okada, Akiyoshi Tsuchiya
{"title":"Two Enriched Poset Polytopes","authors":"Soichi Okada,&nbsp;Akiyoshi Tsuchiya","doi":"10.1007/s00026-023-00679-7","DOIUrl":"10.1007/s00026-023-00679-7","url":null,"abstract":"<div><p>Stanley introduced and studied two lattice polytopes, the order polytope and chain polytope, associated with a finite poset. Recently, Ohsugi and Tsuchiya introduce an enriched version of them, called the enriched order polytope and enriched chain polytope. In this paper, we give a piecewise-linear bijection between these enriched poset polytopes, which is an enriched analogue of Stanley’s transfer map and bijectively proves that they have the same Ehrhart polynomials. Also, we construct explicitly unimodular triangulations of two enriched poset polytopes, which are the order complexes of graded posets.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 1","pages":"257 - 282"},"PeriodicalIF":0.6,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139031804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximate Sampling of Graphs with Near-P-Stable Degree Intervals 近似采样具有近 P 稳定度区间的图
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2023-12-21 DOI: 10.1007/s00026-023-00678-8
Péter L. Erdős, Tamás Róbert Mezei, István Miklós
{"title":"Approximate Sampling of Graphs with Near-P-Stable Degree Intervals","authors":"Péter L. Erdős,&nbsp;Tamás Róbert Mezei,&nbsp;István Miklós","doi":"10.1007/s00026-023-00678-8","DOIUrl":"10.1007/s00026-023-00678-8","url":null,"abstract":"<div><p>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 <i>P</i>-stable degree sequences (see <span>DOI:10.1016/j.ejc.2021.103421</span>). The switch Markov chain does not change any degree sequence. However, there are cases where degree intervals are specified rather than a single degree sequence. (A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed.) Rechner, Strowick, and Müller–Hannemann introduced in 2018 the notion of <i>degree interval Markov chain</i> which uses three (separately well studied) local operations (switch, hinge-flip and toggle), and employing on degree sequence realizations where any two sequences under scrutiny have very small coordinate-wise distance. Recently, Amanatidis and Kleer published a beautiful paper (<span>DOI:10.4230/LIPIcs.STACS.2023.7</span>), showing that the degree interval Markov chain is rapidly mixing if the sequences are coming from a system of very thin intervals which are centered not far from a regular degree sequence. In this paper, we substantially extend their result, showing that the degree interval Markov chain is rapidly mixing if the intervals are centered at <i>P</i>-stable degree sequences.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 1","pages":"223 - 256"},"PeriodicalIF":0.6,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00678-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139017850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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