Advances in Applied Mathematics最新文献

A direct proof of well-definedness for the polymatroid Tutte polynomial 多面体图特多项式定义明确性的直接证明

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-27 DOI: 10.1016/j.aam.2024.102809

Xiaxia Guan , Xian'an Jin

引用次数: 0

Existence of solutions to the even Gaussian dual Minkowski problem 偶数高斯对偶闵科夫斯基问题解的存在性

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-25 DOI: 10.1016/j.aam.2024.102808

Yibin Feng , Shengnan Hu , Lei Xu

{"title":"Existence of solutions to the even Gaussian dual Minkowski problem","authors":"Yibin Feng , Shengnan Hu , Lei Xu","doi":"10.1016/j.aam.2024.102808","DOIUrl":"10.1016/j.aam.2024.102808","url":null,"abstract":"<div><div>In this paper, we consider the Gaussian dual Minkowski problem. The problem involves a new type of fully nonlinear partial differential equations on the unit sphere. Our main purpose is to show the existence of solutions to the even Gaussian dual Minkowski problem for <span><math><mi>q</mi><mo>></mo><mn>0</mn></math></span>. More precisely, we will show that there exists an origin-symmetric convex body <em>K</em> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> such that its Gaussian dual curvature measure <span><math><msub><mrow><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>q</mi></mrow></msub><mo>(</mo><mi>K</mi><mo>,</mo><mo>⋅</mo><mo>)</mo></math></span> has density <em>f</em> (up to a constant) on the unit sphere when <span><math><mi>q</mi><mo>></mo><mn>0</mn></math></span> and <em>f</em> has positive upper and lower bounds. Note that if <em>f</em> is smooth then <em>K</em> is also smooth. As the application of smooth solutions, we completely solve the even Gaussian dual Minkowski problem for <span><math><mi>q</mi><mo>></mo><mn>0</mn></math></span> based on an approximation argument.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"163 ","pages":"Article 102808"},"PeriodicalIF":1.0,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Identifying circular orders for blobs in phylogenetic networks 识别系统发生网络中 Blob 的循环顺序

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-20 DOI: 10.1016/j.aam.2024.102804

John A. Rhodes , Hector Baños , Jingcheng Xu , Cécile Ané

{"title":"Identifying circular orders for blobs in phylogenetic networks","authors":"John A. Rhodes , Hector Baños , Jingcheng Xu , Cécile Ané","doi":"10.1016/j.aam.2024.102804","DOIUrl":"10.1016/j.aam.2024.102804","url":null,"abstract":"<div><div>Interest in the inference of evolutionary networks relating species or populations has grown with the increasing recognition of the importance of hybridization, gene flow and admixture, and the availability of large-scale genomic data. However, what network features may be validly inferred from various data types under different models remains poorly understood. Previous work has largely focused on level-1 networks, in which reticulation events are well separated, and on a general network's tree of blobs, the tree obtained by contracting every blob to a node. An open question is the identifiability of the topology of a blob of unknown level. We consider the identifiability of the circular order in which subnetworks attach to a blob, first proving that this order is well-defined for outer-labeled planar blobs. For this class of blobs, we show that the circular order information from 4-taxon subnetworks identifies the full circular order of the blob. Similarly, the circular order from 3-taxon rooted subnetworks identifies the full circular order of a rooted blob. We then show that subnetwork circular information is identifiable from certain data types and evolutionary models. This provides a general positive result for high-level networks, on the identifiability of the ordering in which taxon blocks attach to blobs in outer-labeled planar networks. Finally, we give examples of blobs with different internal structures which cannot be distinguished under many models and data types.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"163 ","pages":"Article 102804"},"PeriodicalIF":1.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Triangular partitions: Enumeration, structure, and generation 三角形分区：枚举、结构和生成

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-16 DOI: 10.1016/j.aam.2024.102807

Sergi Elizalde , Alejandro B. Galván

{"title":"Triangular partitions: Enumeration, structure, and generation","authors":"Sergi Elizalde , Alejandro B. Galván","doi":"10.1016/j.aam.2024.102807","DOIUrl":"10.1016/j.aam.2024.102807","url":null,"abstract":"<div><div>A <em>triangular partition</em> is a partition whose Ferrers diagram can be separated from its complement (as a subset of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>) by a straight line. Having their origins in combinatorial number theory and computer vision, triangular partitions have been studied from a combinatorial perspective by Onn and Sturmfels, and by Corteel et al. under the name <em>plane corner cuts</em>, and more recently by Bergeron and Mazin in the context of algebraic combinatorics. In this paper we derive new enumerative, geometric and algorithmic properties of such partitions.</div><div>We give a new characterization of triangular partitions and the cells that can be added or removed while preserving the triangular condition, and use it to describe the Möbius function of the restriction of Young's lattice to triangular partitions. We obtain a formula for the number of triangular partitions whose Young diagram fits inside a square, deriving, as a byproduct, a new proof of Lipatov's enumeration theorem for balanced words. Finally, we present an algorithm that generates all the triangular partitions of a given size, which is significantly more efficient than previous ones and allows us to compute the number of triangular partitions of size up to 10<sup>5</sup>.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"163 ","pages":"Article 102807"},"PeriodicalIF":1.0,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Principal specializations of Schubert polynomials, multi-layered permutations and asymptotics 舒伯特多项式的主特殊化、多层排列和渐近论

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-12 DOI: 10.1016/j.aam.2024.102806

Ningxin Zhang

引用次数: 0

Fully graphic degree sequences and P-stable degree sequences 全图形度序列和 P 稳定度序列

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-12 DOI: 10.1016/j.aam.2024.102805

Péter L. Erdős , István Miklós , Lajos Soukup

{"title":"Fully graphic degree sequences and P-stable degree sequences","authors":"Péter L. Erdős , István Miklós , Lajos Soukup","doi":"10.1016/j.aam.2024.102805","DOIUrl":"10.1016/j.aam.2024.102805","url":null,"abstract":"<div><div>The notion of <em>P</em>-stability of an infinite set of degree sequences plays influential role in approximating the permanents, rapidly sampling the realizations of graphic degree sequences, or even studying and improving network privacy. While there exist several known sufficient conditions for <em>P</em>-stability, we don't know any useful necessary condition for it. We also do not have good insight of possible structure of <em>P</em>-stable degree sequence families.</div><div>At first we will show that every known infinite <em>P</em>-stable degree sequence set, described by inequalities of the parameters <span><math><mi>n</mi><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>Σ</mi></math></span> (the sequence length, the maximum and minimum degrees and the sum of the degrees) is “fully graphic” meaning that every degree sequence from the region with an even degree sum, is graphic. Furthermore, if Σ does not occur in the determining inequality, then the notions of <em>P</em>-stability and full graphicality will be proved equivalent. In turn, this equality provides a strengthening of the well-known theorem of Jerrum, McKay and Sinclair about <em>P</em>-stability, describing the maximal <em>P</em>-stable sequence set by <span><math><mi>n</mi><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. Furthermore we conjecture that similar equivalences occur in cases if Σ also part of the defining inequality.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"163 ","pages":"Article 102805"},"PeriodicalIF":1.0,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Non-intersecting path explanation for block Pfaffians and applications into skew-orthogonal polynomials 分块普法因子的非相交路径解释及其在倾斜正交多项式中的应用

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-12 DOI: 10.1016/j.aam.2024.102803

Zong-Jun Yao, Shi-Hao Li

引用次数: 0

Refining a chain theorem from matroids to internally 4-connected graphs 完善从矩阵到内部 4 连接图的链式定理

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-11-06 DOI: 10.1016/j.aam.2024.102802

Chanun Lewchalermvongs , Guoli Ding

引用次数: 0

On the enumeration of series-parallel matroids 关于串并联矩阵的枚举

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-10-30 DOI: 10.1016/j.aam.2024.102801

Nicholas Proudfoot , Yuan Xu , Benjamin Young

引用次数: 0

Identifiability of homoscedastic linear structural equation models using algebraic matroids 利用代数矩阵识别同源线性结构方程模型

IF 1 3区数学

Advances in Applied Mathematics Pub Date : 2024-10-15 DOI: 10.1016/j.aam.2024.102794

Mathias Drton, Benjamin Hollering, Jun Wu

引用次数: 0