Annals of Combinatorics最新文献_第2页

Special Functions for Hyperoctahedral Groups Using Bosonic Lattice Models 基于玻色子晶格模型的超八面体群的特殊函数

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-12-09 DOI: 10.1007/s00026-024-00734-x

Ben Brubaker, Will Grodzicki, Andrew Schultz

引用次数: 0

Words Avoiding Tangrams 避免拼字

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-12-05 DOI: 10.1007/s00026-024-00736-9

Michał Dȩbski, Jarosław Grytczuk, Bartłomiej Pawlik, Jakub Przybyło, Małgorzata Śleszyńska-Nowak

{"title":"Words Avoiding Tangrams","authors":"Michał Dȩbski, Jarosław Grytczuk, Bartłomiej Pawlik, Jakub Przybyło, Małgorzata Śleszyńska-Nowak","doi":"10.1007/s00026-024-00736-9","DOIUrl":"10.1007/s00026-024-00736-9","url":null,"abstract":"<div>A tangram is a word in which every letter occurs an even number of times. Such word can be cut into parts that can be arranged into two identical words. The minimum number of cuts needed is called the cut number of a tangram. For example, the word <img> is a tangram with cut number one, while the word <img> is a tangram with cut number two. Clearly, tangrams with cut number one coincide with the well-known family of words, known as squares, having the form UU for some nonempty word U. A word W avoids a word T if it is not possible to write (W=ATB), for any words A and B (possibly empty). The famous 1906 theorem of Thue asserts that there exist arbitrarily long words avoiding squares over an alphabet with just three letters. Given a fixed number (kgeqslant 1), how many letters are needed to avoid tangrams with the cut number at most k? Let t(k) denote the minimum size of an alphabet needed for that purpose. By Thue’s result we have (t(1)=3), which easily implies (t(2)=3). Curiously, these are currently the only known exact values of this function. In our main result we prove that (t(k)=Theta (log _2k)). The proof uses entropy compression argument and Zimin words. Using a different method we prove that (t(k)leqslant k+1) for all (kgeqslant 4), which gives more exact estimates for small values of k. The proof makes use of Dejean words and a curious property of Gauss words, which is perhaps of independent interest.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"905 - 920"},"PeriodicalIF":0.7,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00736-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037268","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

Planar Binary Trees, Noncrossing Partitions and the Operator-Valued S-Transform 平面二叉树、非交叉划分和算子值s变换

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-11-28 DOI: 10.1007/s00026-024-00730-1

Kurusch Ebrahimi-Fard, Timothé Ringeard

引用次数: 0

General Position Sets, Colinear Sets, and Sierpiński Product Graphs 一般位置集，共线性集，和Sierpiński产品图

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-11-20 DOI: 10.1007/s00026-024-00732-z

Jing Tian, Sandi Klavžar

引用次数: 0

Totally Symmetric Self-Complementary Plane Partition Matrices and Related Polytopes 全对称自互补平面划分矩阵及相关多面体

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-11-18 DOI: 10.1007/s00026-024-00723-0

Vincent Holmlund, Jessica Striker

引用次数: 0

Grand-Schnyder Woods Grand-Schnyder森林

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-11-14 DOI: 10.1007/s00026-024-00729-8

Olivier Bernardi, Éric Fusy, Shizhe Liang

{"title":"Grand-Schnyder Woods","authors":"Olivier Bernardi, Éric Fusy, Shizhe Liang","doi":"10.1007/s00026-024-00729-8","DOIUrl":"10.1007/s00026-024-00729-8","url":null,"abstract":"<div>We define a far-reaching generalization of Schnyder woods which encompasses many classical combinatorial structures on planar graphs. Schnyder woods are defined for planar triangulations as certain triples of spanning trees covering the triangulation and crossing each other in an orderly fashion. They are of theoretical and practical importance, as they are central to the proof that the order dimension of any planar graph is at most 3, and they are also underlying an elegant drawing algorithm. In this article, we extend the concept of Schnyder wood well beyond its original setting: for any integer (dge 3), we define a “grand-Schnyder” structure for (embedded) planar graphs which have faces of degree at most d and non-facial cycles of length at least d. We prove the existence of grand-Schnyder structures, provide a linear construction algorithm, describe 4 different incarnations (in terms of tuples of trees, corner labelings, weighted orientations, and marked orientations), and define a lattice for the set of grand-Schnyder structures of a given planar graph. We show that the grand-Schnyder framework unifies and extends several classical constructions: Schnyder woods and Schnyder decompositions, regular edge-labelings (a.k.a. transversal structures), and Felsner woods.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"273 - 373"},"PeriodicalIF":0.7,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165628","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

On the Correctness of Maximum Parsimony for Data with Few Substitutions in the NNI Neighborhood of Phylogenetic Trees 系统发育树NNI邻域中少量替换数据最大简约性的正确性

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-11-14 DOI: 10.1007/s00026-024-00725-y

Mareike Fischer

{"title":"On the Correctness of Maximum Parsimony for Data with Few Substitutions in the NNI Neighborhood of Phylogenetic Trees","authors":"Mareike Fischer","doi":"10.1007/s00026-024-00725-y","DOIUrl":"10.1007/s00026-024-00725-y","url":null,"abstract":"<div>Estimating phylogenetic trees, which depict the relationships between different species, from aligned sequence data (such as DNA, RNA, or proteins) is one of the main aims of evolutionary biology. However, tree reconstruction criteria like maximum parsimony do not necessarily lead to unique trees and in some cases even fail to recognize the “correct” tree (i.e., the tree on which the data was generated). On the other hand, a recent study has shown that for an alignment containing precisely those binary characters (sites) which require up to two substitutions on a given tree, this tree will be the unique maximum parsimony tree. It is the aim of the present paper to generalize this recent result in the following sense: We show that for a tree T with n leaves, as long as (k<frac{n}{8}+frac{11}{9}-frac{1}{18}sqrt{9cdot left( frac{n}{4}right) ^2+16}) (or, equivalently, (n>9k-11+sqrt{9k^2-22k+17}), which in particular holds for all (nge 12k)), the maximum parsimony tree for the alignment containing all binary characters which require (up to or precisely) k substitutions on T will be unique in the NNI neighborhood of T and it will coincide with T, too. In other words, within the NNI neighborhood of T, T is the unique most parsimonious tree for the said alignment. This partially answers a recently published conjecture affirmatively. Additionally, we show that for (nge 8) and for k being in the order of (frac{n}{2}), there is always a pair of phylogenetic trees T and (T') which are NNI neighbors, but for which the alignment of characters requiring precisely k substitutions each on T in total requires fewer substitutions on (T').</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"615 - 635"},"PeriodicalIF":0.7,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00725-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165625","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

Log-Concavity with Respect to the Number of Orbits for Infinite Tuples of Commuting Permutations 交换置换无限元组关于轨道数的对数凹性

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-11-06 DOI: 10.1007/s00026-024-00724-z

Abdelmalek Abdesselam

{"title":"Log-Concavity with Respect to the Number of Orbits for Infinite Tuples of Commuting Permutations","authors":"Abdelmalek Abdesselam","doi":"10.1007/s00026-024-00724-z","DOIUrl":"10.1007/s00026-024-00724-z","url":null,"abstract":"<div>Let A(p, n, k) be the number of p-tuples of commuting permutations of n elements whose permutation action results in exactly k orbits or connected components. We formulate the conjecture that, for every fixed p and n, the A(p, n, k) form a log-concave sequence with respect to k. For (p=1) this is a well-known property of unsigned Stirling numbers of the first kind. As the (p=2) case, our conjecture includes a previous one by Heim and Neuhauser, which strengthens a unimodality conjecture for the Nekrasov–Okounkov hook length polynomials. In this article, we prove the (p=infty ) case of our conjecture. We start from an expression for the A(p, n, k), which follows from an identity by Bryan and Fulman, obtained in the their study of orbifold higher equivariant Euler characteristics. We then derive the (prightarrow infty ) asymptotics. The last step essentially amounts to the log-concavity in k of a generalized Turán number, namely, the maximum product of k positive integers whose sum is n.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"563 - 573"},"PeriodicalIF":0.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00724-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162896","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 Problem of Douglass and Ono for the Plane Partition Function 平面配分函数的Douglass和Ono问题

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-11-06 DOI: 10.1007/s00026-024-00728-9

Florian Luca

引用次数: 0

Shi Arrangements Restricted to Weyl Cones Shi的安排仅限于Weyl cone

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-10-14 DOI: 10.1007/s00026-024-00720-3

Galen Dorpalen-Barry, Christian Stump

引用次数: 0