Annals of Combinatorics最新文献_第6页

Combinatorics of Euclidean Spaces over Finite Fields 有限域上的欧几里得空间组合学

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-09-20 DOI: 10.1007/s00026-023-00661-3

Semin Yoo

引用次数: 0

Combinatorics of Exterior Peaks on Pattern-Avoiding Symmetric Transversals 规避模式的对称横截面上的外峰组合学

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-09-15 DOI: 10.1007/s00026-023-00664-0

Robin D. P. Zhou, Sherry H. F. Yan

{"title":"Combinatorics of Exterior Peaks on Pattern-Avoiding Symmetric Transversals","authors":"Robin D. P. Zhou, Sherry H. F. Yan","doi":"10.1007/s00026-023-00664-0","DOIUrl":"10.1007/s00026-023-00664-0","url":null,"abstract":"<div>Let (mathcal{S}mathcal{T}_{lambda }(tau )) denote the set of symmetric transversals of a self-conjugate Young diagram (lambda ) which avoid the permutation pattern (tau ). Given two permutations (tau = tau _1tau _2ldots tau _n ) of ({1,2,ldots ,n}) and (sigma =sigma _1sigma _2ldots sigma _m ) of ({1,2,ldots ,m}), the direct sum of (tau ) and (sigma ), denoted by (tau oplus sigma ), is the permutation (tau _1tau _2ldots tau _n (sigma _1+n)(sigma _2+n)ldots (sigma _m+n)). We establish an exterior peak set preserving bijection between (mathcal{S}mathcal{T}_{lambda }(321oplus tau )) and (mathcal{S}mathcal{T}_{lambda }(213oplus tau )) for any pattern (tau ) and any self-conjugate Young diagram (lambda ). Our result is a refinement of part of a result of Bousquet-Mélou–Steingrímsson for pattern-avoiding symmetric transversals. As applications, we derive several enumerative results concerning pattern-avoiding reverse alternating involutions, including two conjectured equalities posed by Barnabei–Bonetti–Castronuovo–Silimbani.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-023-00664-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135395375","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 Consequences of the Valley Delta Conjectures 山谷三角洲猜想的一些结果

4区数学

Annals of Combinatorics Pub Date : 2023-09-11 DOI: 10.1007/s00026-023-00663-1

Michele D’Adderio, Alessandro Iraci

{"title":"Some Consequences of the Valley Delta Conjectures","authors":"Michele D’Adderio, Alessandro Iraci","doi":"10.1007/s00026-023-00663-1","DOIUrl":"https://doi.org/10.1007/s00026-023-00663-1","url":null,"abstract":"Abstract Haglund et al. (Trans Am Math Soc 370(6):4029–4057, 2018) introduced their Delta conjectures , which give two different combinatorial interpretations of the symmetric function $$Delta '_{e_{n-k-1}} e_n$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>e</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>k</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>′</mml:mo> </mml:msubsup> <mml:msub> <mml:mi>e</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:math> in terms of rise-decorated or valley-decorated labelled Dyck paths. While the rise version has been recently proved (D’Adderio and Mellit in Adv Math 402:108342, 2022; Blasiak et al. in A Proof of the Extended Delta Conjecture, arXiv:2102.08815 , 2021), not much is known about the valley version. In this work, we prove the Schröder case of the valley Delta conjecture, the Schröder case of its square version (Iraci and Wyngaerd in Ann Combin 25(1):195–227, 2021), and the Catalan case of its extended version (Qiu and Wilson in J Combin Theory Ser A 175:105271, 2020). Furthermore, assuming the symmetry of (a refinement of) the combinatorial side of the extended valley Delta conjecture, we deduce also the Catalan case of its square version (Iraci and Wyngaerd 2021).","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981269","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 Conjectured Formula for the Rational (varvec{q},varvec{t})-Catalan Polynomial 有理$$varvec{q}，varvec{t}$$-Catalan多项式的一个猜想公式

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-09-07 DOI: 10.1007/s00026-023-00662-2

Graham Hawkes

引用次数: 0

On Distance-Balanced Generalized Petersen Graphs 关于距离平衡广义Petersen图

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-08-17 DOI: 10.1007/s00026-023-00660-4

Gang Ma, Jianfeng Wang, Sandi Klavžar

引用次数: 0

A Murnaghan–Nakayama Rule for Grothendieck Polynomials of Grassmannian Type Grassmann型Grothendieck多项式的Murnaghan–Nakayama规则

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-07-25 DOI: 10.1007/s00026-023-00659-x

Duc-Khanh Nguyen, Dang Tuan Hiep, Tran Ha Son, Do Le Hai Thuy

引用次数: 0

Combinatorial Properties of Three Classical Truncated Theta Series Theorems 三个经典截断Theta级数定理的组合性质

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-07-03 DOI: 10.1007/s00026-023-00658-y

Andrew Y. Z. Wang, Ang Xiao

引用次数: 0

On the Compatible Sets Expansion of the Tutte Polynomial 关于Tutte多项式的相容集展开

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-06-30 DOI: 10.1007/s00026-023-00657-z

Laura Pierson

引用次数: 0

Asymptotics of Multivariate Sequences IV: Generating Functions with Poles on a Hyperplane Arrangement 多变量序列渐近论 IV：超平面排列上有极点的生成函数

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-06-13 DOI: 10.1007/s00026-023-00654-2

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle

引用次数: 0

The Space of Equidistant Phylogenetic Cactuses 等距系统发育仙人掌的空间

IF 0.6 4区数学

Annals of Combinatorics Pub Date : 2023-06-09 DOI: 10.1007/s00026-023-00656-0

Katharina T. Huber, Vincent Moulton, Megan Owen, Andreas Spillner, Katherine St. John

{"title":"The Space of Equidistant Phylogenetic Cactuses","authors":"Katharina T. Huber, Vincent Moulton, Megan Owen, Andreas Spillner, Katherine St. John","doi":"10.1007/s00026-023-00656-0","DOIUrl":"10.1007/s00026-023-00656-0","url":null,"abstract":"<div>An equidistant X-cactus is a type of rooted, arc-weighted, directed acyclic graph with leaf set X, that is used in biology to represent the evolutionary history of a set (X) of species. In this paper, we introduce and investigate the space of equidistant X-cactuses. This space contains, as a subset, the space of ultrametric trees on X that was introduced by Gavryushkin and Drummond. We show that equidistant-cactus space is a CAT(0)-metric space which implies, for example, that there are unique geodesic paths between points. As a key step to proving this, we present a combinatorial result concerning ranked rooted X-cactuses. In particular, we show that such graphs can be encoded in terms of a pairwise compatibility condition arising from a poset of collections of pairs of subsets of (X) that satisfy certain set-theoretic properties. As a corollary, we also obtain an encoding of ranked, rooted X-trees in terms of partitions of X, which provides an alternative proof that the space of ultrametric trees on X is CAT(0). We expect that our results will provide the basis for novel ways to perform statistical analyses on collections of equidistant X-cactuses, as well as new directions for defining and understanding spaces of more general, arc-weighted phylogenetic networks.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10904525/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45787472","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