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An affine isoperimetric inequality for log-concave functions 对数凹函数的仿射等周不等式
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-29 DOI: 10.1016/j.aam.2025.102956
Zengle Zhang , Jiazu Zhou
{"title":"An affine isoperimetric inequality for log-concave functions","authors":"Zengle Zhang ,&nbsp;Jiazu Zhou","doi":"10.1016/j.aam.2025.102956","DOIUrl":"10.1016/j.aam.2025.102956","url":null,"abstract":"<div><div>The authors gave an affine isoperimetric inequality <span><span>[41]</span></span> that gives a lower bound for the volume of a polar body and the equality holds if and only if the body is a simplex. In this paper, we give a functional isoperimetric inequality for log-concave functions that contains the affine isoperimetric inequality of Lutwak, Yang and Zhang in <span><span>[41]</span></span>.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102956"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911887","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
q-Binomial identities finder q-二项式恒等式查找器
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-09-10 DOI: 10.1016/j.aam.2025.102965
Hao Zhong, Leqi Zhao
{"title":"q-Binomial identities finder","authors":"Hao Zhong,&nbsp;Leqi Zhao","doi":"10.1016/j.aam.2025.102965","DOIUrl":"10.1016/j.aam.2025.102965","url":null,"abstract":"<div><div>This paper presents a symbolic computation method for automatically transforming <em>q</em>-hypergeometric identities to <em>q</em>-binomial identities. Through this method, many previously proven <em>q</em>-binomial identities, including <em>q</em>-Saalschütz's formula and <em>q</em>-Suranyi's formula, are re-fund, and numerous new ones are discovered. Moreover, the generation of the identities is accompanied by the corresponding proofs. During the transformation process, different ranges of variable values and various combinations of <em>q</em>-Pochhammer symbols yield different identities. The algorithm maps variable constraints to positive elements in an ordered vector space and employs a backtracking method to provide the feasible variable constraints and <em>q</em>-binomial coefficient combinations for each step.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102965"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026317","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
Representation theory and central limit theorems for traces of commutators for compact Lie groups 紧李群换向子迹的表示理论和中心极限定理
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-22 DOI: 10.1016/j.aam.2025.102962
Jason Fulman
{"title":"Representation theory and central limit theorems for traces of commutators for compact Lie groups","authors":"Jason Fulman","doi":"10.1016/j.aam.2025.102962","DOIUrl":"10.1016/j.aam.2025.102962","url":null,"abstract":"<div><div>There has been some work in the literature on limit theorems for the trace of commutators for compact Lie groups. We revisit this from the perspective of combinatorial representation theory.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102962"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144889329","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
Metrics for classes of semi-binary phylogenetic networks using μ-representations 使用μ表示的半二元系统发育网络类的度量
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-21 DOI: 10.1016/j.aam.2025.102953
Christopher Reichling, Leo van Iersel, Yukihiro Murakami
{"title":"Metrics for classes of semi-binary phylogenetic networks using μ-representations","authors":"Christopher Reichling,&nbsp;Leo van Iersel,&nbsp;Yukihiro Murakami","doi":"10.1016/j.aam.2025.102953","DOIUrl":"10.1016/j.aam.2025.102953","url":null,"abstract":"<div><div>Phylogenetic networks are useful in representing the evolutionary history of taxa. In certain scenarios, one requires a way to compare different networks. In practice, this can be rather difficult, except within specific classes of networks. In this paper, we derive metrics for the class of <em>orchard networks</em> and the class of <em>strongly reticulation-visible</em> networks, from variants of so-called <em>μ-representations</em>, which are vector representations of networks. For both network classes, we impose degree constraints on the vertices, by considering <em>semi-binary</em> networks.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102953"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144878156","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
Counting the number of group orbits by marrying the Burnside process with importance sampling 结合伯恩赛德过程和重要抽样来计算群轨道的数量
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-22 DOI: 10.1016/j.aam.2025.102955
Persi Diaconis , Chenyang Zhong
{"title":"Counting the number of group orbits by marrying the Burnside process with importance sampling","authors":"Persi Diaconis ,&nbsp;Chenyang Zhong","doi":"10.1016/j.aam.2025.102955","DOIUrl":"10.1016/j.aam.2025.102955","url":null,"abstract":"<div><div>This paper introduces a novel and general algorithm for approximately counting the number of orbits under group actions. The method is based on combining the Burnside process and importance sampling. Specializing to unitriangular groups yields an efficient algorithm for estimating the number of conjugacy classes of such groups.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102955"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886384","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
On fractal patterns in Ulam words 论乌兰语词汇的分形模式
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-09-08 DOI: 10.1016/j.aam.2025.102954
Andrei Mandelshtam
{"title":"On fractal patterns in Ulam words","authors":"Andrei Mandelshtam","doi":"10.1016/j.aam.2025.102954","DOIUrl":"10.1016/j.aam.2025.102954","url":null,"abstract":"<div><div>Ulam words are binary words defined recursively as follows: the length-1 Ulam words are 0 and 1, and a binary word of length <em>n</em> is Ulam if and only if it is expressible uniquely as a concatenation of two shorter, distinct Ulam words. We discover, fully describe, and prove a surprisingly rich structure already in the set of Ulam words containing exactly two 1's. In particular, this leads to a complete description of such words and a logarithmic-time algorithm to determine whether a binary word with two 1's is Ulam. Along the way, we uncover delicate parity and biperiodicity properties, as well as sharp bounds on the number of 0's outside the two 1's. We also show that sets of Ulam words indexed by the number <em>y</em> of 0's between the two 1's have intricate tensor-based hierarchical structures determined by the arithmetic properties of <em>y</em>. This allows us to construct an infinite family of self-similar Ulam-word-based fractals indexed by the set of 2-adic integers, containing the outward Sierpinski gasket as a special case.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102954"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010477","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
SL(n) covariant matrix-valued valuations on Orlicz spaces Orlicz空间上的SL(n)协变矩阵值赋值
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-22 DOI: 10.1016/j.aam.2025.102960
Chunna Zeng , Yu Lan
{"title":"SL(n) covariant matrix-valued valuations on Orlicz spaces","authors":"Chunna Zeng ,&nbsp;Yu Lan","doi":"10.1016/j.aam.2025.102960","DOIUrl":"10.1016/j.aam.2025.102960","url":null,"abstract":"<div><div>All continuous, <span><math><mrow><mi>SL</mi></mrow><mo>(</mo><mi>n</mi><mo>)</mo></math></span> covariant valuations on Orlicz spaces are completely classified without any symmetric assumptions. It is shown that the moment matrix is the only such valuation if <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, while a new functional shows up in dimension two.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102960"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886379","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
On the records and zeros of a deterministic random walk 关于确定性随机游走的记录和零点
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-09-09 DOI: 10.1016/j.aam.2025.102963
Henk Bruin, Robbert Fokkink
{"title":"On the records and zeros of a deterministic random walk","authors":"Henk Bruin,&nbsp;Robbert Fokkink","doi":"10.1016/j.aam.2025.102963","DOIUrl":"10.1016/j.aam.2025.102963","url":null,"abstract":"<div><div>We settle two questions on sequence A120243 in the OEIS that were raised by Clark Kimberling and partly solve a conjecture of Van de Lune and Arias de Reyna. We extend Kimberling's questions to the framework of deterministic random walks, automatic sequences, and linear recurrences. Our results indicate that there may be a deeper connection between these structures. In particular, we conjecture that the records of deterministic random walks are <em>ξ</em>-Ostrowski automatic for quadratic rotation numbers <em>ξ</em>.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102963"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019453","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
Coconvex characters on collections of phylogenetic trees 系统发育树集合上的共凸特征
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-19 DOI: 10.1016/j.aam.2025.102952
Eva Czabarka , Steven Kelk , Vincent Moulton , László A. Székely
{"title":"Coconvex characters on collections of phylogenetic trees","authors":"Eva Czabarka ,&nbsp;Steven Kelk ,&nbsp;Vincent Moulton ,&nbsp;László A. Székely","doi":"10.1016/j.aam.2025.102952","DOIUrl":"10.1016/j.aam.2025.102952","url":null,"abstract":"<div><div>In phylogenetics, a key problem is to construct evolutionary trees from collections of characters where, for a set <em>X</em> of species, a character is simply a function from <em>X</em> onto a set of states. In this context, a key concept is convexity, where a character is convex on a tree with leaf set <em>X</em> if the collection of subtrees spanned by the leaves of the tree that have the same state are pairwise disjoint. Although collections of convex characters on a single tree have been extensively studied over the past few decades, very little is known about <em>coconvex characters</em>, that is, characters that are simultaneously convex on a collection of trees. As a starting point to better understand coconvexity, in this paper we prove a number of extremal results for the following question: <em>What is the minimal number of coconvex characters on a collection of n-leaved trees taken over all collections of size</em> <span><math><mi>t</mi><mo>≥</mo><mn>2</mn></math></span><em>, also if we restrict to coconvex characters which map to k states?</em> As an application of coconvexity, we introduce a new one-parameter family of tree metrics, which range between the coarse Robinson-Foulds distance and the much finer quartet distance. We show that bounds on the quantities in the above question translate into bounds for the diameter of the tree space for the new distances. Our results open up several new interesting directions and questions which have potential applications to, for example, tree spaces and phylogenomics.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102952"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865208","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
q-supercongruences for truncated q-Appell series 截断q-Appell级数的q超同余
IF 1.3 3区 数学
Advances in Applied Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-22 DOI: 10.1016/j.aam.2025.102961
Haihong He , Xiaoxia Wang
{"title":"q-supercongruences for truncated q-Appell series","authors":"Haihong He ,&nbsp;Xiaoxia Wang","doi":"10.1016/j.aam.2025.102961","DOIUrl":"10.1016/j.aam.2025.102961","url":null,"abstract":"<div><div>Congruences and <em>q</em>-congruences for the truncated Appell series are quite finite in the literature. In this paper, we introduce the truncated <em>q</em>-Appell series and investigate their congruence properties. Specifically, using two hypergeometric summations, the ‘creative microscoping’ method formulated by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials, we establish some <em>q</em>-supercongruences on the truncated <em>q</em>-Appell series <span><math><msup><mrow><mi>Φ</mi></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>,</mo><msup><mrow><mi>Φ</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msup><mo>,</mo><msup><mrow><mi>Φ</mi></mrow><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></msup></math></span>. Moreover, in terms of the <em>q</em>-Zeilberger algorithm, a <em>q</em>-supercongruence for the truncated <em>q</em>-Appell series <span><math><msup><mrow><mi>Φ</mi></mrow><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></msup></math></span> is built, which is a new <em>q</em>-analogue of a conjecture of Apagodu and Zeilberger. As conclusions, we immediately obtain some congruences of the truncated Appell series.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102961"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886385","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
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