Journal of Combinatorial Theory Series B最新文献

{"title":"On the difference of mean subtree orders under edge contraction","authors":"Ruoyu Wang","doi":"10.1016/j.jctb.2024.06.002","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.06.002","url":null,"abstract":"<div><p>Given a tree <em>T</em> of order <em>n</em>, one can contract any edge and obtain a new tree <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> of order <span><math><mi>n</mi><mo>−</mo><mn>1</mn></math></span>. In 1983, Jamison made a conjecture that the mean subtree order, i.e., the average order of all subtrees, decreases at least <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> in contracting an edge of a tree. In 2023, Luo, Xu, Wagner and Wang proved the case when the edge to be contracted is a pendant edge. In this article, we prove that the conjecture is true in general.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 45-62"},"PeriodicalIF":1.4,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000467/pdfft?md5=bc686935124fe54d5af1a2d92fba12b9&pid=1-s2.0-S0095895624000467-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141422666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Locally finite vertex-rotary maps and coset graphs with finite valency and finite edge multiplicity","authors":"Cai Heng Li ,&nbsp;Cheryl E. Praeger ,&nbsp;Shu Jiao Song","doi":"10.1016/j.jctb.2024.05.005","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.05.005","url":null,"abstract":"<div><p>A well-known theorem of Sabidussi shows that a simple <em>G</em>-arc-transitive graph can be represented as a coset graph for the group <em>G</em>. This pivotal result is the standard way to turn problems about simple arc-transitive graphs into questions about groups. In this paper, the Sabidussi representation is extended to arc-transitive, not necessarily simple graphs which satisfy a local-finiteness condition: namely graphs with finite valency and finite edge-multiplicity. The construction yields a <em>G</em>-arc-transitive coset graph <span><math><mrow><mi>Cos</mi></mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>,</mo><mi>J</mi><mo>)</mo></math></span>, where <span><math><mi>H</mi><mo>,</mo><mi>J</mi></math></span> are stabilisers in <em>G</em> of a vertex and incident edge, respectively. A first major application is presented concerning arc-transitive maps on surfaces: given a group <span><math><mi>G</mi><mo>=</mo><mo>〈</mo><mi>a</mi><mo>,</mo><mi>z</mi><mo>〉</mo></math></span> with <span><math><mo>|</mo><mi>z</mi><mo>|</mo><mo>=</mo><mn>2</mn></math></span> and <span><math><mo>|</mo><mi>a</mi><mo>|</mo></math></span> finite, the coset graph <span><math><mrow><mi>Cos</mi></mrow><mo>(</mo><mi>G</mi><mo>,</mo><mo>〈</mo><mi>a</mi><mo>〉</mo><mo>,</mo><mo>〈</mo><mi>z</mi><mo>〉</mo><mo>)</mo></math></span> is shown, under suitable finiteness assumptions, to have exactly two different arc-transitive embeddings as a <em>G</em>-arc-transitive map <span><math><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> (with <span><math><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>F</mi></math></span> the sets of vertices, edges and faces, respectively), namely, a <em>G-rotary</em> map if <span><math><mo>|</mo><mi>a</mi><mi>z</mi><mo>|</mo></math></span> is finite, and a <em>G-bi-rotary</em> map if <span><math><mo>|</mo><mi>z</mi><msup><mrow><mi>z</mi></mrow><mrow><mi>a</mi></mrow></msup><mo>|</mo></math></span> is finite. The <em>G</em>-rotary map can be represented as a coset geometry for <em>G</em>, extending the notion of a coset graph. However the <em>G</em>-bi-rotary map does not have such a representation, and the face boundary cycles must be specified in addition to incidences between faces and edges. In addition a coset geometry construction is given of a flag-regular map <span><math><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> for non necessarily simple graphs. For all of these constructions it is proved that the face boundary cycles are simple cycles precisely when the given group acts faithfully on <span><math><mi>V</mi><mo>∪</mo><mi>F</mi></math></span>. Illustrative examples are given for graphs related to the <em>n</em>-dimensional hypercubes and the Petersen graph.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 1-44"},"PeriodicalIF":1.4,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141303366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Counting oriented trees in digraphs with large minimum semidegree","authors":"Felix Joos,&nbsp;Jonathan Schrodt","doi":"10.1016/j.jctb.2024.05.004","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.05.004","url":null,"abstract":"<div><p>Let <em>T</em> be an oriented tree on <em>n</em> vertices with maximum degree at most <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>o</mi><mo>(</mo><msqrt><mrow><mi>log</mi><mo>⁡</mo><mi>n</mi></mrow></msqrt><mo>)</mo></mrow></msup></math></span>. If <em>G</em> is a digraph on <em>n</em> vertices with minimum semidegree <span><math><msup><mrow><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo><mi>n</mi></math></span>, then <em>G</em> contains <em>T</em> as a spanning tree, as recently shown by Kathapurkar and Montgomery (in fact, they only require maximum degree <span><math><mi>o</mi><mo>(</mo><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>). This generalizes the corresponding result by Komlós, Sárközy and Szemerédi for graphs. We investigate the natural question how many copies of <em>T</em> the digraph <em>G</em> contains. Our main result states that every such <em>G</em> contains at least <span><math><mo>|</mo><mrow><mi>Aut</mi><mi>(</mi><mi>T</mi><mi>)</mi></mrow><mspace></mspace><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mi>n</mi><mo>!</mo></math></span> copies of <em>T</em>, which is optimal. This implies the analogous result in the undirected case.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 236-270"},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000431/pdfft?md5=7f84c56186e46b0ae787c373b4164785&pid=1-s2.0-S0095895624000431-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The burning number conjecture holds asymptotically","authors":"Sergey Norin,&nbsp;Jérémie Turcotte","doi":"10.1016/j.jctb.2024.05.003","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.05.003","url":null,"abstract":"<div><p>The burning number <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a graph <em>G</em> is the smallest number of turns required to burn all vertices of a graph if at every turn a new fire is started and existing fires spread to all adjacent vertices. The Burning Number Conjecture of Bonato et al. (2016) postulates that <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mrow><mo>⌈</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>⌉</mo></mrow></math></span> for all connected graphs <em>G</em> on <em>n</em> vertices. We prove that this conjecture holds asymptotically, that is <span><math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 208-235"},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Directed cycles with zero weight in Zpk","authors":"Shoham Letzter ,&nbsp;Natasha Morrison","doi":"10.1016/j.jctb.2024.05.002","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.05.002","url":null,"abstract":"<div><p>For a finite abelian group <em>A</em>, define <span><math><mi>f</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> to be the minimum integer such that for every complete digraph Γ on <em>f</em> vertices and every map <span><math><mi>w</mi><mo>:</mo><mi>E</mi><mo>(</mo><mi>Γ</mi><mo>)</mo><mo>→</mo><mi>A</mi></math></span>, there exists a directed cycle <em>C</em> in Γ such that <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mi>C</mi><mo>)</mo></mrow></msub><mi>w</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>. The study of <span><math><mi>f</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> was initiated by Alon and Krivelevich (2021). In this article, we prove that <span><math><mi>f</mi><mo>(</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msubsup><mo>)</mo><mo>=</mo><mi>O</mi><mo>(</mo><mi>p</mi><mi>k</mi><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, where <em>p</em> is prime, with an improved bound of <span><math><mi>O</mi><mo>(</mo><mi>k</mi><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></math></span> when <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>. These bounds are tight up to a factor which is polylogarithmic in <em>k</em>.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 192-207"},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000418/pdfft?md5=5e9d14a46eed8e2ee2946b39a3ab2037&pid=1-s2.0-S0095895624000418-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dirac-type theorems for long Berge cycles in hypergraphs","authors":"Alexandr Kostochka ,&nbsp;Ruth Luo ,&nbsp;Grace McCourt","doi":"10.1016/j.jctb.2024.05.001","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.05.001","url":null,"abstract":"<div><p>The famous Dirac's Theorem gives an exact bound on the minimum degree of an <em>n</em>-vertex graph guaranteeing the existence of a hamiltonian cycle. In the same paper, Dirac also observed that a graph with minimum degree at least <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> contains a cycle of length at least <span><math><mi>k</mi><mo>+</mo><mn>1</mn></math></span>. The purpose of this paper is twofold: we prove exact bounds of similar type for hamiltonian Berge cycles as well as for Berge cycles of length at least <em>k</em> in <em>r</em>-uniform, <em>n</em>-vertex hypergraphs for all combinations of <span><math><mi>k</mi><mo>,</mo><mi>r</mi></math></span> and <em>n</em> with <span><math><mn>3</mn><mo>≤</mo><mi>r</mi><mo>,</mo><mi>k</mi><mo>≤</mo><mi>n</mi></math></span>. The bounds differ for different ranges of <em>r</em> compared to <em>n</em> and <em>k</em>.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 159-191"},"PeriodicalIF":1.4,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141078547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graphs with all holes the same length","authors":"Linda Cook ,&nbsp;Jake Horsfield ,&nbsp;Myriam Preissmann ,&nbsp;Cléophée Robin ,&nbsp;Paul Seymour ,&nbsp;Ni Luh Dewi Sintiari ,&nbsp;Nicolas Trotignon ,&nbsp;Kristina Vušković","doi":"10.1016/j.jctb.2024.04.006","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.04.006","url":null,"abstract":"<div><p>A graph is <em>ℓ-holed</em> if all its induced cycles of length at least four have length exactly <em>ℓ</em>. We give a complete description of the <em>ℓ</em>-holed graphs for each <span><math><mi>ℓ</mi><mo>≥</mo><mn>7</mn></math></span>.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 96-158"},"PeriodicalIF":1.4,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140924613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"No perfect state transfer in trees with more than 3 vertices","authors":"Gabriel Coutinho,&nbsp;Emanuel Juliano,&nbsp;Thomás Jung Spier","doi":"10.1016/j.jctb.2024.04.004","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.04.004","url":null,"abstract":"<div><p>We prove that the only trees that admit perfect state transfer according to the adjacency matrix model are <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>. This answers a question first asked by Godsil in 2012 and proves a conjecture by Coutinho and Liu from 2015.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 68-85"},"PeriodicalIF":1.4,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140901144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chromatic number is not tournament-local","authors":"António Girão ,&nbsp;Kevin Hendrey ,&nbsp;Freddie Illingworth ,&nbsp;Florian Lehner ,&nbsp;Lukas Michel ,&nbsp;Michael Savery ,&nbsp;Raphael Steiner","doi":"10.1016/j.jctb.2024.04.005","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.04.005","url":null,"abstract":"<div><p>Scott and Seymour conjectured the existence of a function <span><math><mi>f</mi><mo>:</mo><mi>N</mi><mo>→</mo><mi>N</mi></math></span> such that, for every graph <em>G</em> and tournament <em>T</em> on the same vertex set, <span><math><mi>χ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>⩾</mo><mi>f</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> implies that <span><math><mi>χ</mi><mo>(</mo><mi>G</mi><mo>[</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>T</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mi>v</mi><mo>)</mo><mo>]</mo><mo>)</mo><mo>⩾</mo><mi>k</mi></math></span> for some vertex <em>v</em>. In this note we disprove this conjecture even if <em>v</em> is replaced by a vertex set of size <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>)</mo></math></span>. As a consequence, we answer in the negative a question of Harutyunyan, Le, Thomassé, and Wu concerning the corresponding statement where the graph <em>G</em> is replaced by another tournament, and disprove a related conjecture of Nguyen, Scott, and Seymour. We also show that the setting where chromatic number is replaced by degeneracy exhibits a quite different behaviour.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 86-95"},"PeriodicalIF":1.4,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000315/pdfft?md5=96fc5d216231691bd8b06b1f5ac0f4bd&pid=1-s2.0-S0095895624000315-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140900886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Embedding loose spanning trees in 3-uniform hypergraphs","authors":"Yanitsa Pehova ,&nbsp;Kalina Petrova","doi":"10.1016/j.jctb.2024.04.003","DOIUrl":"https://doi.org/10.1016/j.jctb.2024.04.003","url":null,"abstract":"<div><p>In 1995, Komlós, Sárközy and Szemerédi showed that every large <em>n</em>-vertex graph with minimum degree at least <span><math><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>γ</mi><mo>)</mo><mi>n</mi></math></span> contains all spanning trees of bounded degree. We consider a generalization of this result to loose spanning hypertrees in 3-graphs, that is, linear hypergraphs obtained by successively appending edges sharing a single vertex with a previous edge. We show that for all <em>γ</em> and Δ, and <em>n</em> large, every <em>n</em>-vertex 3-uniform hypergraph of minimum vertex degree <span><math><mo>(</mo><mn>5</mn><mo>/</mo><mn>9</mn><mo>+</mo><mi>γ</mi><mo>)</mo><mrow><mo>(</mo><mtable><mtr><mtd><mi>n</mi></mtd></mtr><mtr><mtd><mn>2</mn></mtd></mtr></mtable><mo>)</mo></mrow></math></span> contains every loose spanning tree <em>T</em> with maximum vertex degree Δ. This bound is asymptotically tight, since some loose trees contain perfect matchings.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 47-67"},"PeriodicalIF":1.4,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000303/pdfft?md5=4e333586884c0a88ecc3b2284d18ce92&pid=1-s2.0-S0095895624000303-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}