European Journal of Combinatorics最新文献

{"title":"A note on the singularity probability of random directed d-regular graphs","authors":"Hoi H. Nguyen,&nbsp;Amanda Pan","doi":"10.1016/j.ejc.2024.104039","DOIUrl":"10.1016/j.ejc.2024.104039","url":null,"abstract":"<div><p>In this note we show that the singular probability of the adjacency matrix of a random <span><math><mi>d</mi></math></span>-regular graph on <span><math><mi>n</mi></math></span> vertices, where <span><math><mi>d</mi></math></span> is fixed and <span><math><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, is bounded by <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>+</mo><mi>o</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup></math></span>. This improves a recent bound by Huang in Huang (2021). Our method is based on the study of the singularity problem modulo a prime developed in Huang (2021) (and also partially in Mészáros, 2021; Nguyen and Wood, 2018), together with an inverse-type result on the decay of the characteristic function. The latter is related to the inverse Kneser’s problem in combinatorics.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141951724","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":"Normal 5-edge-coloring of some snarks superpositioned by Flower snarks","authors":"Jelena Sedlar ,&nbsp;Riste Škrekovski","doi":"10.1016/j.ejc.2024.104038","DOIUrl":"10.1016/j.ejc.2024.104038","url":null,"abstract":"<div><p>An edge <span><math><mi>e</mi></math></span> is normal in a proper edge-coloring of a cubic graph <span><math><mi>G</mi></math></span> if the number of distinct colors on four edges incident to <span><math><mi>e</mi></math></span> is 2 or <span><math><mrow><mn>4</mn><mo>.</mo></mrow></math></span> A normal edge-coloring of <span><math><mi>G</mi></math></span> is a proper edge-coloring in which every edge of <span><math><mi>G</mi></math></span> is normal. The Petersen Coloring Conjecture is equivalent to stating that every bridgeless cubic graph has a normal 5-edge-coloring. Since every 3-edge-coloring of a cubic graph is trivially normal, it is sufficient to consider only snarks to establish the conjecture. In this paper, we consider a class of superpositioned snarks obtained by choosing a cycle <span><math><mi>C</mi></math></span> in a snark <span><math><mi>G</mi></math></span> and superpositioning vertices of <span><math><mi>C</mi></math></span> by one of two simple supervertices and edges of <span><math><mi>C</mi></math></span> by superedges <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></msub></math></span>, where <span><math><mi>H</mi></math></span> is any snark and <span><math><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></math></span> any pair of nonadjacent vertices of <span><math><mrow><mi>H</mi><mo>.</mo></mrow></math></span> For such superpositioned snarks, two sufficient conditions are given for the existence of a normal 5 -edge-coloring. The first condition yields a normal 5-edge-coloring for all hypohamiltonian snarks used as superedges, but only for some of the possible ways of connecting them. In particular, since the Flower snarks are hypohamiltonian, this consequently yields a normal 5-edge-coloring for many snarks superpositioned by the Flower snarks. The second sufficient condition is more demanding, but its application yields a normal 5-edge-colorings for all superpositions by the Flower snarks. The same class of snarks is considered in <em>Liu et al. (2021)</em> for the Berge–Fulkerson conjecture. Since we established that this class has a Petersen coloring, this immediately yields the result of the above mentioned paper.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141951725","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":"Hadwiger’s conjecture and topological bounds","authors":"Raphael Steiner","doi":"10.1016/j.ejc.2024.104033","DOIUrl":"10.1016/j.ejc.2024.104033","url":null,"abstract":"<div><p>The Odd Hadwiger’s conjecture, formulated by Gerards and Seymour in 1995, is a substantial strengthening of Hadwiger’s famous coloring conjecture from 1943. We investigate whether the hierarchy of topological lower bounds on the chromatic number, introduced by Matoušek and Ziegler (2003) and refined recently by Daneshpajouh and Meunier (2023), forms a potential avenue to a disproof of Hadwiger’s conjecture or its odd-minor variant. In this direction, we prove that, in a very general sense, every graph <span><math><mi>G</mi></math></span> that admits a topological lower bound of <span><math><mi>t</mi></math></span> on its chromatic number, contains <span><math><msub><mrow><mi>K</mi></mrow><mrow><mrow><mo>⌊</mo><mi>t</mi><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow><mo>+</mo><mn>1</mn></mrow></msub></math></span> as an odd-minor. This solves a problem posed by Simonyi and Zsbán (2010).</p><p>We also prove that if for a graph <span><math><mi>G</mi></math></span> the Dol’nikov-Kříž lower bound on the chromatic number (one of the lower bounds in the aforementioned hierarchy) attains a value of at least <span><math><mi>t</mi></math></span>, then <span><math><mi>G</mi></math></span> contains <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> as a minor.</p><p>Finally, extending results by Simonyi and Zsbán, we show that the Odd Hadwiger’s conjecture holds for Schrijver and Kneser graphs for any choice of the parameters. The latter are canonical examples of graphs for which topological lower bounds on the chromatic number are tight.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001185/pdfft?md5=fa3d2810594b912d86c5d392d33bb225&pid=1-s2.0-S0195669824001185-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141951723","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":"Precoloring extension of Vizing’s Theorem for multigraphs","authors":"Yan Cao ,&nbsp;Guantao Chen ,&nbsp;Guangming Jing ,&nbsp;Xuli Qi ,&nbsp;Songling Shan","doi":"10.1016/j.ejc.2024.104037","DOIUrl":"10.1016/j.ejc.2024.104037","url":null,"abstract":"<div><p>Let <span><math><mi>G</mi></math></span> be a graph with maximum degree <span><math><mrow><mi>Δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and maximum multiplicity <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. Vizing and Gupta, independently, proved in the 1960s that the chromatic index of <span><math><mi>G</mi></math></span> is at most <span><math><mrow><mi>Δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><mi>μ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. The distance between two edges <span><math><mi>e</mi></math></span> and <span><math><mi>f</mi></math></span> in <span><math><mi>G</mi></math></span> is the length of a shortest path connecting an endvertex of <span><math><mi>e</mi></math></span> and an endvertex of <span><math><mi>f</mi></math></span>. A distance-<span><math><mi>t</mi></math></span> matching is a set of edges having pairwise distance at least <span><math><mi>t</mi></math></span>. Albertson and Moore conjectured that if <span><math><mi>G</mi></math></span> is a simple graph, using the palette <span><math><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>Δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn><mo>}</mo></mrow></math></span>, any precoloring on a distance-3 matching can be extended to a proper edge coloring of <span><math><mi>G</mi></math></span>. Edwards et al. proposed the following stronger conjecture: For any graph <span><math><mi>G</mi></math></span>, using the palette <span><math><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>Δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><mi>μ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>}</mo></mrow></math></span>, any precoloring on a distance-2 matching can be extended to a proper edge coloring of <span><math><mi>G</mi></math></span>. Girão and Kang verified the conjecture of Edwards et al. for distance-9 matchings. In this paper, we improve the required distance from 9 to 3 for multigraphs <span><math><mi>G</mi></math></span> with <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≥</mo><mn>2</mn></mrow></math></span>.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141950562","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":"Graphs with no even holes and no sector wheels are the union of two chordal graphs","authors":"Tara Abrishami ,&nbsp;Eli Berger ,&nbsp;Maria Chudnovsky ,&nbsp;Shira Zerbib","doi":"10.1016/j.ejc.2024.104035","DOIUrl":"10.1016/j.ejc.2024.104035","url":null,"abstract":"<div><p>Sivaraman (2020) conjectured that if <span><math><mi>G</mi></math></span> is a graph with no induced even cycle then there exist sets <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> satisfying <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∪</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> such that the induced graphs <span><math><mrow><mi>G</mi><mrow><mo>[</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>]</mo></mrow></mrow></math></span> and <span><math><mrow><mi>G</mi><mrow><mo>[</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></mrow></mrow></math></span> are both chordal. We prove this conjecture in the special case where <span><math><mi>G</mi></math></span> contains no sector wheel, namely, a pair <span><math><mrow><mo>(</mo><mi>H</mi><mo>,</mo><mi>w</mi><mo>)</mo></mrow></math></span> where <span><math><mi>H</mi></math></span> is an induced cycle of <span><math><mi>G</mi></math></span> and <span><math><mi>w</mi></math></span> is a vertex in <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>∖</mo><mi>V</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span> such that <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>∩</mo><mi>H</mi></mrow></math></span> is either <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span> or a path with at least three vertices.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141950563","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":"Combinatorial generation via permutation languages. VI. Binary trees","authors":"Petr Gregor ,&nbsp;Torsten Mütze ,&nbsp;Namrata","doi":"10.1016/j.ejc.2024.104020","DOIUrl":"10.1016/j.ejc.2024.104020","url":null,"abstract":"<div><p>In this paper we propose a notion of pattern avoidance in binary trees that generalizes the avoidance of contiguous tree patterns studied by Rowland and non-contiguous tree patterns studied by Dairyko, Pudwell, Tyner, and Wynn. Specifically, we propose algorithms for generating different classes of binary trees that are characterized by avoiding one or more of these generalized patterns. This is achieved by applying the recent Hartung–Hoang–Mütze–Williams generation framework, by encoding binary trees via permutations. In particular, we establish a one-to-one correspondence between tree patterns and certain mesh permutation patterns. We also conduct a systematic investigation of all tree patterns on at most 5 vertices, and we establish bijections between pattern-avoiding binary trees and other combinatorial objects, in particular pattern-avoiding lattice paths and set partitions.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001057/pdfft?md5=0f21619605d14f0f464a0bba55039445&pid=1-s2.0-S0195669824001057-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141729129","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":"Subdivisions in dicritical digraphs with large order or digirth","authors":"Lucas Picasarri-Arrieta,&nbsp;Clément Rambaud","doi":"10.1016/j.ejc.2024.104022","DOIUrl":"10.1016/j.ejc.2024.104022","url":null,"abstract":"<div><p>Aboulker et al. proved that a digraph with large enough dichromatic number contains any fixed digraph as a subdivision. The dichromatic number of a digraph is the smallest order of a partition of its vertex set into acyclic induced subdigraphs. A digraph is dicritical if the removal of any arc or vertex decreases its dichromatic number. In this paper we give sufficient conditions on a dicritical digraph of large order or large directed girth to contain a given digraph as a subdivision. In particular, we prove that (i) for every integers <span><math><mrow><mi>k</mi><mo>,</mo><mi>ℓ</mi></mrow></math></span>, large enough dicritical digraphs with dichromatic number <span><math><mi>k</mi></math></span> contain an orientation of a cycle with at least <span><math><mi>ℓ</mi></math></span> vertices; (ii) there are functions <span><math><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></math></span> such that for every subdivision <span><math><msup><mrow><mi>F</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> of a digraph <span><math><mi>F</mi></math></span>, digraphs with directed girth at least <span><math><mrow><mi>f</mi><mrow><mo>(</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span> and dichromatic number at least <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> contain a subdivision of <span><math><msup><mrow><mi>F</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>, and if <span><math><mi>F</mi></math></span> is a tree, then <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>F</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>|</mo><mi>V</mi><mrow><mo>(</mo><mi>F</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math></span>; (iii) there is a function <span><math><mi>f</mi></math></span> such that for every subdivision <span><math><msup><mrow><mi>F</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> of <span><math><mrow><mi>T</mi><msub><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> (the transitive tournament on three vertices), digraphs with directed girth at least <span><math><mrow><mi>f</mi><mrow><mo>(</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span> and minimum out-degree at least 2 contain <span><math><msup><mrow><mi>F</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> as a subdivision.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141630308","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":"Enumerating regions of Shi arrangements per Weyl cone","authors":"Aram Dermenjian ,&nbsp;Eleni Tzanaki","doi":"10.1016/j.ejc.2024.104002","DOIUrl":"https://doi.org/10.1016/j.ejc.2024.104002","url":null,"abstract":"<div><p>Given a Shi arrangement <span><math><msub><mrow><mo>Shi</mo></mrow><mrow><mi>Φ</mi></mrow></msub></math></span>, it is well-known that the total number of regions is counted by the parking number of type <span><math><mi>Φ</mi></math></span> and the total number of regions in the dominant cone is given by the Catalan number of type <span><math><mi>Φ</mi></math></span>. In the case of the latter, in Shi (1997), Shi gave a bijection between antichains in the root poset of <span><math><mi>Φ</mi></math></span> and the regions in the dominant cone. This result was later extended by Armstrong, Reiner and Rhoades in Armstrong et al. (2015) where they gave a bijection between the number of regions contained in an arbitrary Weyl cone <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>w</mi></mrow></msub></math></span> in <span><math><msub><mrow><mo>Shi</mo></mrow><mrow><mi>Φ</mi></mrow></msub></math></span> and certain subposets of the root poset. In this article we expand on these results by giving a determinantal formula for the precise number of regions in <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>w</mi></mrow></msub></math></span> using paths in certain digraphs related to Shi diagrams.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824000878/pdfft?md5=ab820f1a5561b5235bb9cad9f35e2215&pid=1-s2.0-S0195669824000878-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141539893","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":"Skew symplectic and orthogonal characters through lattice paths","authors":"Seamus P. Albion ,&nbsp;Ilse Fischer ,&nbsp;Hans Höngesberg ,&nbsp;Florian Schreier-Aigner","doi":"10.1016/j.ejc.2024.104000","DOIUrl":"https://doi.org/10.1016/j.ejc.2024.104000","url":null,"abstract":"<div><p>The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi–Trudi formula and the Lascoux–Pragacz formula, the latter being a skew analogue of the Giambelli identity. Comparatively, the skew characters of the symplectic and orthogonal groups, also known as the skew symplectic and orthogonal Schur functions, have received less attention in this direction. We establish analogues of the dual Jacobi–Trudi and Lascoux–Pragacz formulae for these characters. Our approach is entirely combinatorial, being based on lattice path descriptions of the tableaux models of Koike and Terada. Ordinary Jacobi–Trudi formulae are then derived in an algebraic manner from their duals.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824000854/pdfft?md5=27fd60792f502dd428590e06520747af&pid=1-s2.0-S0195669824000854-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141539894","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":"Linear extensions and continued fractions","authors":"Swee Hong Chan ,&nbsp;Igor Pak","doi":"10.1016/j.ejc.2024.104018","DOIUrl":"https://doi.org/10.1016/j.ejc.2024.104018","url":null,"abstract":"<div><p>We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given number of linear extensions.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001033/pdfft?md5=54c557aaf8c82af5cc506fbf46b6ca94&pid=1-s2.0-S0195669824001033-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479934","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}