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On the Number of Neighborly Simplices in (mathbb {R}^d) 论$$mathbb {R}^d$$ 中的邻简数目
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-05-06 DOI: 10.1007/s00026-024-00694-2
Andrzej P. Kisielewicz
{"title":"On the Number of Neighborly Simplices in (mathbb {R}^d)","authors":"Andrzej P. Kisielewicz","doi":"10.1007/s00026-024-00694-2","DOIUrl":"10.1007/s00026-024-00694-2","url":null,"abstract":"<div><p>Two <i>d</i>-dimensional simplices in <span>(mathbb {R}^d)</span> are neighborly if its intersection is a <span>((d-1))</span>-dimensional set. A family of <i>d</i>-dimensional simplices in <span>(mathbb {R}^d)</span> is called neighborly if every two simplices of the family are neighborly. Let <span>(S_d)</span> be the maximal cardinality of a neighborly family of <i>d</i>-dimensional simplices in <span>(mathbb {R}^d)</span>. Based on the structure of some codes <span>(Vsubset {0,1,*}^n)</span> it is shown that <span>(lim _{drightarrow infty }(2^{d+1}-S_d)=infty )</span>. Moreover, a result on the structure of codes <span>(Vsubset {0,1,*}^n)</span> is given.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00694-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885752","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
On a Conjecture on Pattern-Avoiding Machines 关于模式规避机的猜想
IF 0.5 4区 数学
Annals of Combinatorics Pub Date : 2024-04-18 DOI: 10.1007/s00026-024-00693-3
Christopher Bao, Giulio Cerbai, Yunseo Choi, Katelyn Gan, Owen Zhang
{"title":"On a Conjecture on Pattern-Avoiding Machines","authors":"Christopher Bao, Giulio Cerbai, Yunseo Choi, Katelyn Gan, Owen Zhang","doi":"10.1007/s00026-024-00693-3","DOIUrl":"https://doi.org/10.1007/s00026-024-00693-3","url":null,"abstract":"<p>Let <i>s</i> be West’s stack-sorting map, and let <span>(s_{T})</span> be the generalized stack-sorting map, where instead of being required to increase, the stack avoids subpermutations that are order-isomorphic to any permutation in the set <i>T</i>. In 2020, Cerbai, Claesson, and Ferrari introduced the <span>(sigma )</span>-machine <span>(s circ s_{sigma })</span> as a generalization of West’s 2-stack-sorting-map <span>(s circ s)</span>. As a further generalization, in 2021, Baril, Cerbai, Khalil, and Vajnovski introduced the <span>((sigma , tau ))</span>-machine <span>(s circ s_{sigma , tau })</span> and enumerated <span>(textrm{Sort}_{n}(sigma ,tau ))</span>—the number of permutations in <span>(S_n)</span> that are mapped to the identity by the <span>((sigma , tau ))</span>-machine—for six pairs of length 3 permutations <span>((sigma , tau ))</span>. In this work, we settle a conjecture by Baril, Cerbai, Khalil, and Vajnovski on the only remaining pair of length 3 patterns <span>((sigma , tau ) = (132, 321))</span> for which <span>(|textrm{Sort}_{n}(sigma , tau )|)</span> appears in the OEIS. In addition, we enumerate <span>(textrm{Sort}_n(123, 321))</span>, which does not appear in the OEIS, but has a simple closed form.</p>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140623223","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
Fully Complementary Higher Dimensional Partitions 完全互补的高维分区
IF 0.5 4区 数学
Annals of Combinatorics Pub Date : 2024-04-06 DOI: 10.1007/s00026-024-00691-5
{"title":"Fully Complementary Higher Dimensional Partitions","authors":"","doi":"10.1007/s00026-024-00691-5","DOIUrl":"https://doi.org/10.1007/s00026-024-00691-5","url":null,"abstract":"<h3>Abstract</h3> <p>We introduce a symmetry class for higher dimensional partitions—<em>fully complementary higher dimensional partitions</em> (FCPs)—and prove a formula for their generating function. By studying symmetry classes of FCPs in dimension 2, we define variations of the classical symmetry classes for plane partitions. As a by-product, we obtain conjectures for three new symmetry classes of plane partitions and prove that another new symmetry class, namely <em>quasi-transpose-complementary plane partitions</em>, are equinumerous to symmetric plane partitions.</p>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586291","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
Runs and RSK Tableaux of Boolean Permutations 布尔排列的运行和 RSK 表法
IF 0.5 4区 数学
Annals of Combinatorics Pub Date : 2024-04-04 DOI: 10.1007/s00026-024-00689-z
{"title":"Runs and RSK Tableaux of Boolean Permutations","authors":"","doi":"10.1007/s00026-024-00689-z","DOIUrl":"https://doi.org/10.1007/s00026-024-00689-z","url":null,"abstract":"<h3>Abstract</h3> <p>We define and construct the “canonical reduced word” of a boolean permutation, and show that the RSK tableaux for that permutation can be read off directly from this reduced word. We also describe those tableaux that can correspond to boolean permutations, and enumerate them. In addition, we generalize a result of Mazorchuk and Tenner, showing that the “run” statistic influences the shape of the RSK tableau of arbitrary permutations, not just of those that are boolean.</p>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602418","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
Polynomization of the Bessenrodt–Ono Type Inequalities for A-Partition Functions A 分区函数的贝森罗德-奥诺型不等式的多项式化
IF 0.5 4区 数学
Annals of Combinatorics Pub Date : 2024-04-03 DOI: 10.1007/s00026-024-00692-4
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser
{"title":"Polynomization of the Bessenrodt–Ono Type Inequalities for A-Partition Functions","authors":"Krystian Gajdzica, Bernhard Heim, Markus Neuhauser","doi":"10.1007/s00026-024-00692-4","DOIUrl":"https://doi.org/10.1007/s00026-024-00692-4","url":null,"abstract":"<p>For an arbitrary set or multiset <i>A</i> of positive integers, we associate the <i>A</i>-partition function <span>(p_A(n))</span> (that is the number of partitions of <i>n</i> whose parts belong to <i>A</i>). We also consider the analogue of the <i>k</i>-colored partition function, namely, <span>(p_{A,-k}(n))</span>. Further, we define a family of polynomials <span>(f_{A,n}(x))</span> which satisfy the equality <span>(f_{A,n}(k)=p_{A,-k}(n))</span> for all <span>(nin mathbb {Z}_{ge 0})</span> and <span>(kin mathbb {N})</span>. This paper concerns a polynomialization of the Bessenrodt–Ono inequality, namely </p><span>$$begin{aligned} f_{A,a}(x)f_{A,b}(x)&gt;f_{A,a+b}(x), end{aligned}$$</span><p>where <i>a</i>, <i>b</i> are positive integers. We determine efficient criteria for the solutions of this inequality. Moreover, we also investigate a few basic properties related to both functions <span>(f_{A,n}(x))</span> and <span>(f_{A,n}'(x))</span>.</p>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586393","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
Some Infinite-Dimensional Representations of Certain Coxeter Groups 某些柯克西特群的一些无穷维表示
IF 0.5 4区 数学
Annals of Combinatorics Pub Date : 2024-03-25 DOI: 10.1007/s00026-024-00690-6
Hongsheng Hu
{"title":"Some Infinite-Dimensional Representations of Certain Coxeter Groups","authors":"Hongsheng Hu","doi":"10.1007/s00026-024-00690-6","DOIUrl":"https://doi.org/10.1007/s00026-024-00690-6","url":null,"abstract":"<p>A Coxeter group admits infinite-dimensional irreducible complex representations if and only if it is not finite or affine. In this paper, we provide a construction of some of those representations for certain Coxeter groups using some topological information of the corresponding Coxeter graphs.</p>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301791","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
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":null,"pages":null},"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 0.5 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, Xiaowei Lin","doi":"10.1007/s00026-024-00688-0","DOIUrl":"https://doi.org/10.1007/s00026-024-00688-0","url":null,"abstract":"<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>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"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 0.5 4区 数学
Annals of Combinatorics Pub Date : 2024-02-29 DOI: 10.1007/s00026-024-00687-1
{"title":"Turán Problems for Oriented Graphs","authors":"","doi":"10.1007/s00026-024-00687-1","DOIUrl":"https://doi.org/10.1007/s00026-024-00687-1","url":null,"abstract":"<h3>Abstract</h3> <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 <em>H</em> as a subgraph. It is well-known that the chromatic number of <em>H</em> 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>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.5,"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":null,"pages":null},"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
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