{"title":"Random walks, equidistribution and graphical designs","authors":"Stefan Steinerberger, Rekha R. Thomas","doi":"10.1016/j.aam.2024.102837","DOIUrl":"10.1016/j.aam.2024.102837","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> be a <em>d</em>-regular graph on <em>n</em> vertices and let <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> be a probability measure on <em>V</em>. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on <em>V</em> given by <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>A</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msub><mrow><mi>μ</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>, where <em>A</em> is the adjacency matrix and <em>D</em> is the diagonal matrix of vertex degrees of <em>G</em>. Ordering the eigenvalues of <span><math><mi>A</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> as <span><math><mn>1</mn><mo>=</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo><mo>≥</mo><mo>…</mo><mo>≥</mo><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>|</mo><mo>≥</mo><mn>0</mn></math></span>, it is well-known that the graphs for which <span><math><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo></math></span> is small are those in which the random walk process converges quickly to the uniform distribution: for all initial probability measures <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and all <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>,<span><span><span><math><munder><mo>∑</mo><mrow><mi>v</mi><mo>∈</mo><mi>V</mi></mrow></munder><msup><mrow><mo>|</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>≤</mo><msubsup><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn><mi>k</mi></mrow></msubsup><mo>.</mo></math></span></span></span> One could wonder whether this rate can be improved for specific initial probability measures <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. We show that if <em>G</em> is regular, then for any <span><math><mn>1</mn><mo>≤</mo><mi>ℓ</mi><mo>≤</mo><mi>n</mi></math></span>, there exists a probability measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> supported on at most <em>ℓ</em> vertices so that<span><span><span><math><munder><mo>∑</mo><mrow><mi>v</mi><mo>∈</mo><mi>V</mi></mrow></munder><msup><mrow><mo>|</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>≤</mo><msubsup><mrow><mi>λ</mi></mro","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"165 ","pages":"Article 102837"},"PeriodicalIF":1.0,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143156468","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}
{"title":"The fundamental group in discrete homotopy theory","authors":"Krzysztof Kapulkin, Udit Mavinkurve","doi":"10.1016/j.aam.2024.102838","DOIUrl":"10.1016/j.aam.2024.102838","url":null,"abstract":"<div><div>We develop a robust foundation for studying the fundamental group(oid) in A-homotopy theory, including: equivalent definitions and basic properties, the theory of covering graphs, and the discrete version of the Seifert–van Kampen theorem.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102838"},"PeriodicalIF":1.0,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154466","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}
Shi-Hao Li , Bo-Jian Shen , Guo-Fu Yu , Peter J. Forrester
{"title":"Discrete orthogonal ensemble on the exponential lattices","authors":"Shi-Hao Li , Bo-Jian Shen , Guo-Fu Yu , Peter J. Forrester","doi":"10.1016/j.aam.2024.102836","DOIUrl":"10.1016/j.aam.2024.102836","url":null,"abstract":"<div><div>Inspired by Aomoto's <em>q</em>-Selberg integral, a study is made of an orthogonal ensemble on an exponential lattice. By introducing a skew symmetric kernel, the configuration space of this ensemble is constructed to be symmetric and thus the corresponding skew inner product, skew orthogonal polynomials as well as correlation functions are explicitly formulated. These involve polynomials from the Askey scheme. Examples considered include the Al-Salam & Carlitz, <em>q</em>-Laguerre, little <em>q</em>-Jacobi and big <em>q</em>-Jacobi cases.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102836"},"PeriodicalIF":1.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154467","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}
{"title":"Cells of fixed height in Catalan words and restricted growth functions","authors":"Aubrey Blecher, Arnold Knopfmacher","doi":"10.1016/j.aam.2024.102835","DOIUrl":"10.1016/j.aam.2024.102835","url":null,"abstract":"<div><div>A word <span><math><mi>w</mi><mo>=</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> of length <em>n</em> over the set of positive integers is called a Catalan word whenever <span><math><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span> and <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><mn>1</mn></math></span> for <span><math><mi>k</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi></math></span>. A restricted growth function is defined as a word <span><math><mi>w</mi><mo>=</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> of length <em>n</em> over the set of positive integers where <span><math><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span> and for <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> we have <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≤</mo><mi>max</mi><mo></mo><mo>{</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>}</mo><mo>+</mo><mn>1</mn></math></span>. We also define cells and heights of cells and we represent such words as bargraphs (otherwise known as polyominoes) where the <em>i</em>th column contains <span><math><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> cells for <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>n</mi></math></span> and where all columns have their bottom cell on the <em>x</em>-axis. In the case of Catalan words, we prove a relationship between the number of cells at different heights and first terms of the expanded polynomial <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup></math></span>. In the case of restricted growth functions we find polynomials <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span> where the coefficient of <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msup></math></span> counts the number of cells of height <em>j</em> across all rgfs with <em>n</em> parts. In this case we also find bivariate generating functions for rgfs with <em>k</em> blocks, where the generating functions tracks the number of cells at a given height as well as the number of parts.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102835"},"PeriodicalIF":1.0,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154472","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}
{"title":"Conditions for virtually Cohen–Macaulay simplicial complexes","authors":"Adam Van Tuyl , Jay Yang","doi":"10.1016/j.aam.2024.102830","DOIUrl":"10.1016/j.aam.2024.102830","url":null,"abstract":"<div><div>A simplicial complex Δ is a virtually Cohen–Macaulay simplicial complex if its associated Stanley-Reisner ring <em>S</em> has a virtual resolution, as defined by Berkesch, Erman, and Smith, of length <span><math><mrow><mi>codim</mi></mrow><mo>(</mo><mi>S</mi><mo>)</mo></math></span>. We provide a sufficient condition on Δ to be a virtually Cohen–Macaulay simplicial complex. We also introduce virtually shellable simplicial complexes, a generalization of shellable simplicial complexes. Virtually shellable complexes have the property that they are virtually Cohen–Macaulay, generalizing the well-known fact that shellable simplicial complexes are Cohen–Macaulay.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102830"},"PeriodicalIF":1.0,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154474","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}
{"title":"Dynamics of pop-tsack torsing","authors":"Anqi Li","doi":"10.1016/j.aam.2024.102826","DOIUrl":"10.1016/j.aam.2024.102826","url":null,"abstract":"<div><div>For a finite irreducible Coxeter group <span><math><mo>(</mo><mi>W</mi><mo>,</mo><mi>S</mi><mo>)</mo></math></span> with a fixed Coxeter element <em>c</em> and set of reflections <em>T</em>, Defant and Williams define a pop-tsack torsing operation <span><math><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow><mo>:</mo><mi>W</mi><mo>→</mo><mi>W</mi></math></span> given by <span><math><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow><mo>(</mo><mi>w</mi><mo>)</mo><mo>=</mo><mi>w</mi><mo>⋅</mo><mi>π</mi><msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> where <span><math><mi>π</mi><mo>(</mo><mi>w</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mo>⋁</mo></mrow><mrow><mi>t</mi><msub><mrow><mo>≤</mo></mrow><mrow><mi>T</mi></mrow></msub><mi>w</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>∈</mo><mi>T</mi></mrow><mrow><mi>N</mi><mi>C</mi><mo>(</mo><mi>w</mi><mo>,</mo><mi>c</mi><mo>)</mo></mrow></msubsup><mi>t</mi></math></span> is the join of all reflections lying below <em>w</em> in the absolute order in the non-crossing partition lattice <span><math><mi>N</mi><mi>C</mi><mo>(</mo><mi>w</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></span>. This is a “dual” notion of the pop-stack sorting operator <span><math><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></math></span>; <span><math><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></math></span> was introduced by Defant as a way to generalize the pop-stack sorting operator on <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> to general Coxeter groups. Define the forward orbit of an element <span><math><mi>w</mi><mo>∈</mo><mi>W</mi></math></span> to be <span><math><msub><mrow><mi>O</mi></mrow><mrow><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></mrow></msub><mo>(</mo><mi>w</mi><mo>)</mo><mo>=</mo><mo>{</mo><mi>w</mi><mo>,</mo><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow><mo>(</mo><mi>w</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>w</mi><mo>)</mo><mo>,</mo><mo>…</mo><mo>}</mo></math></span>. Defant and Williams established the length of the longest possible forward orbits <span><math><msub><mrow><mi>max</mi></mrow><mrow><mi>w</mi><mo>∈</mo><mi>W</mi></mrow></msub><mo></mo><mo>|</mo><msub><mrow><mi>O</mi></mrow><mrow><mrow><mi>Po</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></mrow></msub><mo>(</mo><mi>w</mi><mo>)</mo><mo>|</mo></math></span> for Coxeter groups of coincidental types and Type D in terms of the corresponding Coxeter number of the group. In their paper, they also proposed multiple conjectures about enumerating elements with near maximal orbit length. We resolve all the ","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102826"},"PeriodicalIF":1.0,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154477","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}
{"title":"Letter frequency vs factor frequency in pure morphic words","authors":"Shuo Li","doi":"10.1016/j.aam.2024.102834","DOIUrl":"10.1016/j.aam.2024.102834","url":null,"abstract":"<div><div>We prove that, for any pure morphic word <em>w</em>, if the frequencies of all letters in <em>w</em> exist, then the frequencies of all factors in <em>w</em> exist as well. This result answers a question of Saari in his doctoral thesis.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102834"},"PeriodicalIF":1.0,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154470","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}
{"title":"Initial values of ML-degree polynomials","authors":"Maciej Gałązka","doi":"10.1016/j.aam.2024.102831","DOIUrl":"10.1016/j.aam.2024.102831","url":null,"abstract":"<div><div>We prove a conjecture about the initial values of ML-degree polynomials stated by Michałek, Monin, and Wiśniewski.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102831"},"PeriodicalIF":1.0,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154473","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}
{"title":"Chordal matroids arising from generalized parallel connections II","authors":"James Dylan Douthitt, James Oxley","doi":"10.1016/j.aam.2024.102833","DOIUrl":"10.1016/j.aam.2024.102833","url":null,"abstract":"<div><div>In 1961, Dirac showed that chordal graphs are exactly the graphs that can be constructed from complete graphs by a sequence of clique-sums. In an earlier paper, by analogy with Dirac's result, we introduced the class of <span><math><mi>G</mi><mi>F</mi><mo>(</mo><mi>q</mi><mo>)</mo></math></span>-chordal matroids as those matroids that can be constructed from projective geometries over <span><math><mi>G</mi><mi>F</mi><mo>(</mo><mi>q</mi><mo>)</mo></math></span> by a sequence of generalized parallel connections across projective geometries over <span><math><mi>G</mi><mi>F</mi><mo>(</mo><mi>q</mi><mo>)</mo></math></span>. Our main result showed that when <span><math><mi>q</mi><mo>=</mo><mn>2</mn></math></span>, such matroids have no induced minor in <span><math><mo>{</mo><mi>M</mi><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo><mo>,</mo><mi>M</mi><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo><mo>}</mo></math></span>. In this paper, we show that the class of <span><math><mi>G</mi><mi>F</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>-chordal matroids coincides with the class of binary matroids that have none of <span><math><mi>M</mi><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo></math></span>, <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>)</mo></math></span>, or <span><math><mi>M</mi><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span> as a flat. We also show that <span><math><mi>G</mi><mi>F</mi><mo>(</mo><mi>q</mi><mo>)</mo></math></span>-chordal matroids can be characterized by an analogous result to Rose's 1970 characterization of chordal graphs as those that have a perfect elimination ordering of vertices.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102833"},"PeriodicalIF":1.0,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154471","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}
{"title":"Consecutive pattern containment and c-Wilf equivalence","authors":"Reza Rastegar","doi":"10.1016/j.aam.2024.102829","DOIUrl":"10.1016/j.aam.2024.102829","url":null,"abstract":"<div><div>We offer elementary proofs for several results in consecutive pattern containment that were previously demonstrated using ideas from cluster method and analytical combinatorics. Furthermore, we establish new general bounds on the growth rates of consecutive pattern avoidance in permutations.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"164 ","pages":"Article 102829"},"PeriodicalIF":1.0,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153922","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}
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