Advances in Applied Mathematics最新文献_第9页

Block-counting sequences are not purely morphic 块计数序列并非纯粹的形态序列

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2024-02-01 DOI: 10.1016/j.aam.2024.102673

Antoine Abram , Yining Hu , Shuo Li

引用次数: 0

Connectivity of old and new models of friends-and-strangers graphs 新旧朋友和陌生人图谱模型的连接性

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2024-01-16 DOI: 10.1016/j.aam.2023.102668

Aleksa Milojević

引用次数: 0

Generating functions and counting formulas for spanning trees and forests in hypergraphs 超图中生成树和森林的生成函数和计数公式

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2024-01-16 DOI: 10.1016/j.aam.2023.102667

Jiuqiang Liu , Shenggui Zhang , Guihai Yu

引用次数: 0

Rowmotion Markov chains 行运动马尔科夫链

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2024-01-12 DOI: 10.1016/j.aam.2023.102666

Colin Defant , Rupert Li , Evita Nestoridi

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引用次数: 0

Equidistribution of set-valued statistics on standard Young tableaux and transversals 标准扬台和横轴上的集值统计等分布

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2024-01-09 DOI: 10.1016/j.aam.2023.102669

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

引用次数: 0

Moments of permutation statistics and central limit theorems 置换统计矩和中心极限定理

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2024-01-05 DOI: 10.1016/j.aam.2023.102650

Stoyan Dimitrov , Niraj Khare

{"title":"Moments of permutation statistics and central limit theorems","authors":"Stoyan Dimitrov , Niraj Khare","doi":"10.1016/j.aam.2023.102650","DOIUrl":"https://doi.org/10.1016/j.aam.2023.102650","url":null,"abstract":"<div>We show that if a permutation statistic can be written as a linear combination of bivincular patterns, then its moments can be expressed as a linear combination of factorials with constant coefficients. This generalizes a result of Zeilberger. We use an approach of Chern, Diaconis, Kane and Rhoades, previously applied on set partitions and matchings. In addition, we give a new proof of the central limit theorem (CLT) for the number of occurrences of classical patterns, which uses a lemma of Burstein and Hästö. We give a simple interpretation of this lemma and an analogous lemma that would imply the CLT for the number of occurrences of any vincular pattern. Furthermore, we obtain explicit formulas for the moments of the descents and the minimal descents statistics. The latter is used to give a new direct proof of the fact that we do not necessarily have asymptotic normality of the number of pattern occurrences in the case of bivincular patterns. Closed forms for some of the higher moments of several popular statistics on permutations are also obtained.</div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"155 ","pages":"Article 102650"},"PeriodicalIF":1.1,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139107280","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

Pseudo-cones 伪锥体

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2024-01-04 DOI: 10.1016/j.aam.2023.102657

Rolf Schneider

引用次数: 0

Identities and periodic oscillations of divide-and-conquer recurrences splitting at half 分而治之递推规律的同一性和周期性振荡的一半分裂

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2023-12-29 DOI: 10.1016/j.aam.2023.102653

Hsien-Kuei Hwang , Svante Janson , Tsung-Hsi Tsai

{"title":"Identities and periodic oscillations of divide-and-conquer recurrences splitting at half","authors":"Hsien-Kuei Hwang , Svante Janson , Tsung-Hsi Tsai","doi":"10.1016/j.aam.2023.102653","DOIUrl":"10.1016/j.aam.2023.102653","url":null,"abstract":"<div>We study divide-and-conquer recurrences of the form<math><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>α</mi><mi>f</mi><mo>(</mo><mo>⌊</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo><mo>)</mo><mo>+</mo><mi>β</mi><mi>f</mi><mo>(</mo><mo>⌈</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo><mo>)</mo><mo>+</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo><mspace></mspace><mo>(</mo><mi>n</mi><mo>⩾</mo><mn>2</mn><mo>)</mo><mo>,</mo></math> with <math><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> and <math><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> given, where <math><mi>α</mi><mo>,</mo><mi>β</mi><mo>⩾</mo><mn>0</mn></math> with <math><mi>α</mi><mo>+</mo><mi>β</mi><mo>></mo><mn>0</mn></math>; such recurrences appear often in the analysis of computer algorithms, numeration systems, combinatorial sequences, and related areas. We show under an optimum (iff) condition on <math><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> that the solution f always satisfies a simple identity<math><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>n</mi></mrow><mrow><msub><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⁡</mo><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow></msup><mi>P</mi><mo>(</mo><msub><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⁡</mo><mi>n</mi><mo>)</mo><mo>−</mo><mi>Q</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>,</mo></math> where P is a periodic function and <math><mi>Q</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> is of a smaller order than the dominant term. This form is thus not only an identity but also an asymptotic expansion. Explicit forms for the continuity of the periodic function P are provided, together with a few other smoothness properties. We show how our results can be easily applied to many dozens of concrete examples collected from the literature, and how they can be extended in various directions. Our method of proof is surprisingly simple and elementary, but leads to the strongest types of results for all examples to which our theory applies.</div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"155 ","pages":"Article 102653"},"PeriodicalIF":1.1,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139062060","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

Positivity of Narayana polynomials and Eulerian polynomials 纳拉亚纳多项式和欧拉多项式的正相关性

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2023-12-28 DOI: 10.1016/j.aam.2023.102656

Shi-Mei Ma , Hao Qi , Jean Yeh , Yeong-Nan Yeh

引用次数: 0

An inversion statistic on the generalized symmetric groups 广义对称群的反转统计量

IF 1.1 3区数学

Advances in Applied Mathematics Pub Date : 2023-12-22 DOI: 10.1016/j.aam.2023.102655

Hasan Arslan , Alnour Altoum , Mariam Zaarour

引用次数: 0