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Orientable Vertex Primitive Complete Maps 可定向顶点原始完整映射
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-10-07 DOI: 10.1007/s00026-024-00721-2
Xue Yu, Cai Heng Li, Ben Gong Lou
{"title":"Orientable Vertex Primitive Complete Maps","authors":"Xue Yu,&nbsp;Cai Heng Li,&nbsp;Ben Gong Lou","doi":"10.1007/s00026-024-00721-2","DOIUrl":"10.1007/s00026-024-00721-2","url":null,"abstract":"<div><p>An orientable vertex primitive complete map is a two-cell embedding of a complete graph into an orientable surface such that the automorphism group of this map acts primitively on its vertex set. The paper is devoted to the problem of enumerating orientable vertex primitive complete maps. For a given integer <i>n</i>, we derive the number of different such maps with <i>n</i> vertices. Furthermore, we obtain explicit formulas for the numbers of non-isomorphic orientable vertex primitive complete maps with <i>n</i> vertices.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1127 - 1139"},"PeriodicalIF":0.6,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672350","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
Polyhedra with Hexagonal and Triangular Faces and Three Faces Around Each Vertex 具有六边形和三角形面的多面体，每个顶点周围有三个面
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2024-10-07 DOI: 10.1007/s00026-024-00722-1
Linda Green, Stellen Li
{"title":"Polyhedra with Hexagonal and Triangular Faces and Three Faces Around Each Vertex","authors":"Linda Green,&nbsp;Stellen Li","doi":"10.1007/s00026-024-00722-1","DOIUrl":"10.1007/s00026-024-00722-1","url":null,"abstract":"<div><p>We analyze polyhedra composed of hexagons and triangles with three faces around each vertex, and their 3-regular planar graphs of edges and vertices, which we call “trihexes”. Trihexes are analogous to fullerenes, which are 3-regular planar graphs whose faces are all hexagons and pentagons. Every trihex can be represented as the quotient of a hexagonal tiling of the plane under a group of isometries generated by <span>(180^circ )</span> rotations. Every trihex can also be described with either one or three “signatures”: triples of numbers that describe the arrangement of the rotocenters of these rotations. Simple arithmetic rules relate the three signatures that describe the same trihex. We obtain a bijection between trihexes and equivalence classes of signatures as defined by these rules. Labeling trihexes with signatures allows us to put bounds on the number of trihexes for a given number of vertices <i>v</i> in terms of the prime factorization of <i>v</i> and to prove a conjecture concerning trihexes that have no “belts” of hexagons.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"461 - 490"},"PeriodicalIF":0.7,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00722-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163140","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 Determinantal Formula for Orthosymplectic Schur Functions 正辛舒尔函数的行列式
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2024-09-28 DOI: 10.1007/s00026-024-00718-x
Nishu Kumari
{"title":"A Determinantal Formula for Orthosymplectic Schur Functions","authors":"Nishu Kumari","doi":"10.1007/s00026-024-00718-x","DOIUrl":"10.1007/s00026-024-00718-x","url":null,"abstract":"<div><p>We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J Algebraic Combin 17(3):283–307, 2003) for general linear Lie superalgebras. Our proof uses the Jacobi–Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent Math 92(2):307–332, 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J Combin Theory Ser A 144:80–138, 2016).</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"719 - 741"},"PeriodicalIF":0.7,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037420","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
Publisher Correction to: An Asymptotic Lower Bound on the Number of Polyominoes 出版者对：多面体数量的渐近下限
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-09-17 DOI: 10.1007/s00026-024-00710-5
Vuong Bui
{"title":"Publisher Correction to: An Asymptotic Lower Bound on the Number of Polyominoes","authors":"Vuong Bui","doi":"10.1007/s00026-024-00710-5","DOIUrl":"10.1007/s00026-024-00710-5","url":null,"abstract":"","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1363 - 1363"},"PeriodicalIF":0.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672352","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
Efficient Representation of Lattice Path Matroids 高效表示网格路径矩阵
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2024-08-29 DOI: 10.1007/s00026-024-00716-z
Carles Padró
{"title":"Efficient Representation of Lattice Path Matroids","authors":"Carles Padró","doi":"10.1007/s00026-024-00716-z","DOIUrl":"10.1007/s00026-024-00716-z","url":null,"abstract":"<div><p>Efficient deterministic algorithms to construct representations of lattice path matroids over finite fields are presented. They are built on known constructions of hierarchical secret sharing schemes, a recent characterization of hierarchical matroid ports, and the existence of isolating weight functions for lattice path matroids whose values are polynomial on the size of the ground set.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"601 - 614"},"PeriodicalIF":0.7,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203277","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
Partitions with Fixed Points in the Sequence of First-Column Hook Lengths 第一列钩码长度序列中具有固定点的分区
IF 0.5 4区 数学
Annals of Combinatorics Pub Date : 2024-08-09 DOI: 10.1007/s00026-024-00714-1
Philip Cuthbertson, David J. Hemmer, Brian Hopkins, William J. Keith
{"title":"Partitions with Fixed Points in the Sequence of First-Column Hook Lengths","authors":"Philip Cuthbertson, David J. Hemmer, Brian Hopkins, William J. Keith","doi":"10.1007/s00026-024-00714-1","DOIUrl":"https://doi.org/10.1007/s00026-024-00714-1","url":null,"abstract":"<p>Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as <i>h</i>-fixed points for an integer parameter <i>h</i> by Hopkins and Sellers. Here, we consider the sequence of first column hook lengths in the Young diagram of a partition and corresponding <i>fixed hooks</i>. We enumerate these, using both generating function and combinatorial proofs, and find that they match occurrences of part sizes equal to their multiplicity. We establish connections to work of Andrews and Merca on truncations of the pentagonal number theorem and classes of partitions partially characterized by certain minimal excluded parts (mex).</p>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"12 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940741","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
Acyclic Reorientation Lattices and Their Lattice Quotients 无环重定向点阵及其点阵之商
IF 0.6 4区 数学
Annals of Combinatorics Pub Date : 2024-08-09 DOI: 10.1007/s00026-024-00697-z
Vincent Pilaud
{"title":"Acyclic Reorientation Lattices and Their Lattice Quotients","authors":"Vincent Pilaud","doi":"10.1007/s00026-024-00697-z","DOIUrl":"10.1007/s00026-024-00697-z","url":null,"abstract":"<div><p>We prove that the acyclic reorientation poset of a directed acyclic graph <i>D</i> is a lattice if and only if the transitive reduction of any induced subgraph of <i>D</i> is a forest. We then show that the acyclic reorientation lattice is always congruence normal, semidistributive (thus congruence uniform) if and only if <i>D</i> is filled, and distributive if and only if <i>D</i> is a forest. When the acyclic reorientation lattice is semidistributive, we introduce the ropes of <i>D</i> that encode the join irreducible acyclic reorientations and exploit this combinatorial model in three directions. First, we describe the canonical join and meet representations of acyclic reorientations in terms of non-crossing rope diagrams. Second, we describe the congruences of the acyclic reorientation lattice in terms of lower ideals of a natural subrope order. Third, we use Minkowski sums of shard polytopes of ropes to construct a quotientope for any congruence of the acyclic reorientation lattice.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1035 - 1092"},"PeriodicalIF":0.6,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00697-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940742","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 the Support of Grothendieck Polynomials 论格罗内迪克多项式的支持度
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2024-08-08 DOI: 10.1007/s00026-024-00712-3
Karola Mészáros, Linus Setiabrata, Avery St. Dizier
{"title":"On the Support of Grothendieck Polynomials","authors":"Karola Mészáros,&nbsp;Linus Setiabrata,&nbsp;Avery St. Dizier","doi":"10.1007/s00026-024-00712-3","DOIUrl":"10.1007/s00026-024-00712-3","url":null,"abstract":"<div><p>Grothendieck polynomials <span>(mathfrak {G}_w)</span> of permutations <span>(win S_n)</span> were introduced by Lascoux and Schützenberger (C R Acad Sci Paris Sér I Math 295(11):629–633, 1982) as a set of distinguished representatives for the K-theoretic classes of Schubert cycles in the K-theory of the flag variety of <span>(mathbb {C}^n)</span>. We conjecture that the exponents of nonzero terms of the Grothendieck polynomial <span>(mathfrak {G}_w)</span> form a poset under componentwise comparison that is isomorphic to an induced subposet of <span>(mathbb {Z}^n)</span>. When <span>(win S_n)</span> avoids a certain set of patterns, we conjecturally connect the coefficients of <span>(mathfrak {G}_w)</span> with the Möbius function values of the aforementioned poset with <span>(hat{0})</span> appended. We prove special cases of our conjectures for Grassmannian and fireworks permutations</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"541 - 562"},"PeriodicalIF":0.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940740","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 Multiparameter Refinement of Euler’s Theorem 欧拉定理的多参数完善
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2024-08-08 DOI: 10.1007/s00026-024-00713-2
Andrew Y. Z. Wang, Lei Zhang
{"title":"A Multiparameter Refinement of Euler’s Theorem","authors":"Andrew Y. Z. Wang,&nbsp;Lei Zhang","doi":"10.1007/s00026-024-00713-2","DOIUrl":"10.1007/s00026-024-00713-2","url":null,"abstract":"<div><p>Euler’s partition theorem states that every integer has as many partitions into odd parts as into distinct parts. In this work, we reveal a new result behind this statement. On one hand, we study the partitions into odd parts according to the residue modulo 4 of the size of those parts occurring an odd number of times. On the other hand, we discuss the partitions into distinct parts with respect to the position of odd parts in the sequence. Some other statistics are also considered together, including the length, alternating sum and minimal odd excludant.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"743 - 760"},"PeriodicalIF":0.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141928424","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
Sequential Stub Matching for Asymptotically Uniform Generation of Directed Graphs with a Given Degree Sequence 渐近均匀生成给定度序列有向图的序列存根匹配
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2024-08-07 DOI: 10.1007/s00026-024-00715-0
Femke van Ieperen, Ivan Kryven
{"title":"Sequential Stub Matching for Asymptotically Uniform Generation of Directed Graphs with a Given Degree Sequence","authors":"Femke van Ieperen,&nbsp;Ivan Kryven","doi":"10.1007/s00026-024-00715-0","DOIUrl":"10.1007/s00026-024-00715-0","url":null,"abstract":"<div><p>We discuss sequential stub matching for directed graphs and show that this process can be used to sample simple digraphs with asymptotically equal probability. The process starts with an empty edge set and repeatedly adds edges to it with a certain state-dependent bias until the desired degree sequence is fulfilled, whilst avoiding placing a double edge or self-loop. We show that uniform sampling is achieved in the sparse regime when the maximum degree <span>(d_text {max})</span> is asymptotically dominated by <span>(m^{1/4})</span>, where <i>m</i> is the number of edges. The proof is based on deriving various combinatorial estimates related to the number of digraphs with a given degree sequence and controlling concentration of these estimates in large digraphs. This suggests that sequential stub matching can be viewed as a practical algorithm for almost uniform sampling of digraphs. We show that this algorithm can be implemented to feature a linear expected runtime <i>O</i>(<i>m</i>).</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"227 - 272"},"PeriodicalIF":0.7,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00715-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940743","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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