Combinatorica最新文献

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On r-wise t-intersecting Uniform Families 关于向r- t相交的统一族
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-08-07 DOI: 10.1007/s00493-025-00166-y
Peter Frankl, Jian Wang
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引用次数: 0
Spanning Spheres in Dirac Hypergraphs 狄拉克超图中的跨球
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-08-07 DOI: 10.1007/s00493-025-00169-9
Freddie Illingworth, Richard Lang, Alp Müyesser, Olaf Parczyk, Amedeo Sgueglia
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引用次数: 0
An Approximate Counting Version of the Multidimensional Szemerédi Theorem 多维szemersamedi定理的近似计数形式
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-07-23 DOI: 10.1007/s00493-025-00167-x
Natalie Behague, Joseph Hyde, Natasha Morrison, Jonathan A. Noel, Ashna Wright
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引用次数: 0
Set System Blowups 设置系统爆炸
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-07-23 DOI: 10.1007/s00493-025-00163-1
Ryan Alweiss
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引用次数: 0
Subdivisions and near-linear stable sets 细分与近线性稳定集
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-07-04 DOI: 10.1007/s00493-025-00154-2
Tung Nguyen, Alex Scott, Paul Seymour
{"title":"Subdivisions and near-linear stable sets","authors":"Tung Nguyen, Alex Scott, Paul Seymour","doi":"10.1007/s00493-025-00154-2","DOIUrl":"https://doi.org/10.1007/s00493-025-00154-2","url":null,"abstract":"&lt;p&gt;We prove that for every complete graph &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.213ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -735.2 1205.1 952.8\" width=\"2.799ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1201\" xlink:href=\"#MJMATHI-74\" y=\"-213\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;K_t&lt;/script&gt;&lt;/span&gt;, all graphs &lt;i&gt;G&lt;/i&gt; with no induced subgraph isomorphic to a subdivision of &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.213ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -735.2 1205.1 952.8\" width=\"2.799ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1201\" xlink:href=\"#MJMATHI-74\" y=\"-213\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;K_t&lt;/script&gt;&lt;/span&gt; have a stable subset of size at least &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 6664.3 1125.3\" width=\"15.479ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-7C\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"278\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1065\" xlink:href=\"#MJMAIN-7C\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1343\" xlink:href=\"#MJMAIN-2F\" y=\"0\"&gt;&lt;/use&gt;&lt;g transform=\"translate(2010,0)\"&gt;&lt;use xlink:href=\"#MJMAIN-70\"&gt;&lt;/use&gt;&lt;use x=\"556\" xlink:href=\"#MJMAIN-6F\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1057\" xlink:href=\"#MJMAIN-6C\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1335\" xlink:href=\"#MJMAIN-79\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1864\" xlink:href=\"#MJMAIN-6C\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2142\" xlink:href=\"#MJMAIN-6F\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2643\" xlink:href=\"#MJMAIN-67\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;use x=\"5320\" xlink:href=\"#MJMAIN-7C\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"5599\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"6385\" xlink:href=\"#MJMAIN-7C\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;|G|/operatorname {polylog}|G|&lt;/script&gt;&lt;/span&gt;. This is close to best possible, because for &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.209ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -733.9 2196.1 951.2\" width=\"5.101ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-74\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"639\" xlink:href=\"#MJMAIN-2265\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1695\" xlink:href=\"#MJMAIN-37\" y=\"0\"&gt;&lt;/use&gt;&lt;","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"62 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Signed graphs with the same even cycles 具有相同偶数环的符号图
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-07-04 DOI: 10.1007/s00493-025-00160-4
Bertrand Guenin, Cheolwon Heo, Irene Pivotto
{"title":"Signed graphs with the same even cycles","authors":"Bertrand Guenin, Cheolwon Heo, Irene Pivotto","doi":"10.1007/s00493-025-00160-4","DOIUrl":"https://doi.org/10.1007/s00493-025-00160-4","url":null,"abstract":"<p>Whitney proved that if two 3-connected graphs <i>G</i> and <span><span style=\"\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msup&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;&amp;#x2032;&lt;/mo&gt;&lt;/msup&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"2.113ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -821.4 1081.3 909.7\" width=\"2.511ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1112\" xlink:href=\"#MJMAIN-2032\" y=\"513\"></use></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>G</mi><mo>′</mo></msup></math></span></span><script type=\"math/tex\">G'</script></span> have the same set of cycles (or equivalently, the same set of cuts) then <span><span style=\"\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;&amp;#x2032;&lt;/mo&gt;&lt;/msup&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"2.113ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -821.4 3201.9 909.7\" width=\"7.437ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use x=\"1064\" xlink:href=\"#MJMAIN-3D\" y=\"0\"></use><g transform=\"translate(2120,0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1112\" xlink:href=\"#MJMAIN-2032\" y=\"513\"></use></g></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>G</mi><mo>=</mo><msup><mi>G</mi><mo>′</mo></msup></math></span></span><script type=\"math/tex\">G=G'</script></span>. We characterize when two 4-connected signed graphs have the same set of even cycles, and we characterize when two 4-connected grafts have the same set of even cuts.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"24 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Fractional Chromatic Number Vs. Hall Ratio 分数色数与霍尔比
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-07-04 DOI: 10.1007/s00493-025-00164-0
Raphael Steiner
{"title":"Fractional Chromatic Number Vs. Hall Ratio","authors":"Raphael Steiner","doi":"10.1007/s00493-025-00164-0","DOIUrl":"https://doi.org/10.1007/s00493-025-00164-0","url":null,"abstract":"&lt;p&gt;Given a graph &lt;i&gt;G&lt;/i&gt;, its &lt;i&gt;Hall ratio&lt;/i&gt; &lt;span&gt;&lt;span style=\"\"&gt;rho (G)=max _{Hsubseteq G}frac{|V(H)|}{alpha (H)}&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"4.216ex\" role=\"img\" style=\"vertical-align: -1.507ex;\" viewbox=\"0 -1166.4 9758.2 1815.3\" width=\"22.664ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-3C1\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"517\" xlink:href=\"#MJMAIN-28\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"907\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1693\" xlink:href=\"#MJMAIN-29\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2360\" xlink:href=\"#MJMAIN-3D\" y=\"0\"&gt;&lt;/use&gt;&lt;g transform=\"translate(3417,0)\"&gt;&lt;use xlink:href=\"#MJMAIN-6D\"&gt;&lt;/use&gt;&lt;use x=\"833\" xlink:href=\"#MJMAIN-61\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1334\" xlink:href=\"#MJMAIN-78\" y=\"0\"&gt;&lt;/use&gt;&lt;g transform=\"translate(1862,-155)\"&gt;&lt;use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-48\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"888\" xlink:href=\"#MJMAIN-2286\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1667\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/g&gt;&lt;g transform=\"translate(7114,0)\"&gt;&lt;g transform=\"translate(286,0)\"&gt;&lt;rect height=\"60\" stroke=\"none\" width=\"2237\" x=\"0\" y=\"220\"&gt;&lt;/rect&gt;&lt;g transform=\"translate(60,568)\"&gt;&lt;use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMAIN-7C\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"278\" xlink:href=\"#MJMATHI-56\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1048\" xlink:href=\"#MJMAIN-28\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1437\" xlink:href=\"#MJMATHI-48\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"2326\" xlink:href=\"#MJMAIN-29\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"2715\" xlink:href=\"#MJMAIN-7C\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"translate(302,-422)\"&gt;&lt;use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-3B1\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"640\" xlink:href=\"#MJMAIN-28\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1030\" xlink:href=\"#MJMATHI-48\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"1918\" xlink:href=\"#MJMAIN-29\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;rho (G)=max _{Hsubseteq G}frac{|V(H)|}{alpha (H)}&lt;/script&gt;&lt;/span&gt; forms a natural lower bound for its fractional chromatic number &lt;span&gt;&lt;span style=\"\"&gt;chi _f(G)&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.714ex\" role=\"img\" style=\"vertical-align: -0.806ex;\" viewbox=\"0 -821.4 2681.3 1168.4\" width=\"6.227ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-3C7\" y=\"0\"&gt;&lt;/use&gt;&lt;use transform=\"scale(0.707)\" x=\"886\" xlink:href=\"#MJMATHI-66\" y=\"-219\"&gt;&lt;/use&gt;&lt;use x=\"1115\" xlink:href=\"#MJMAIN-28\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1505\" xlink:href=\"#MJMATHI-47\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2291\" xlink:href=\"#MJMAIN-29\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;chi _f(G)&lt;/script&gt;&lt;/s","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"13 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Fat Minors in Finitely Presented Groups 有限呈现组中的肥胖未成年人
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-07-04 DOI: 10.1007/s00493-025-00165-z
Joseph Paul MacManus
{"title":"Fat Minors in Finitely Presented Groups","authors":"Joseph Paul MacManus","doi":"10.1007/s00493-025-00165-z","DOIUrl":"https://doi.org/10.1007/s00493-025-00165-z","url":null,"abstract":"<p>We show that a finitely presented group virtually admits a planar Cayley graph if and only if it is asymptotically minor-excluded, partially answering a conjecture of Georgakopoulos and Papasoglu in the affirmative.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"31 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Partitioning a tournament into sub-tournaments of high connectivity 将锦标赛划分为高连通性的子锦标赛
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-06-23 DOI: 10.1007/s00493-025-00161-3
António Girão, Shoham Letzter
{"title":"Partitioning a tournament into sub-tournaments of high connectivity","authors":"António Girão, Shoham Letzter","doi":"10.1007/s00493-025-00161-3","DOIUrl":"https://doi.org/10.1007/s00493-025-00161-3","url":null,"abstract":"<p>We prove that there exists a constant <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"1.912ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -735.2 2268.1 823.4\" width=\"5.268ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-63\" y=\"0\"></use><use x=\"711\" xlink:href=\"#MJMAIN-3E\" y=\"0\"></use><use x=\"1767\" xlink:href=\"#MJMAIN-30\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">c > 0</script></span> such that the vertices of every strongly <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.013ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -778.3 2039.4 866.5\" width=\"4.737ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-63\" y=\"0\"></use><use x=\"655\" xlink:href=\"#MJMAIN-22C5\" y=\"0\"></use><use x=\"1156\" xlink:href=\"#MJMATHI-6B\" y=\"0\"></use><use x=\"1677\" xlink:href=\"#MJMATHI-74\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">c cdot kt</script></span>-connected tournament can be partitioned into <i>t</i> parts, each of which induces a strongly <i>k</i>-connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of Kühn, Osthus and Townsend (2016).</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"38 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Local h-polynomials, Uniform Triangulations and Real-rootedness 局部h多项式,一致三角剖分与实数根
IF 1.1 2区 数学
Combinatorica Pub Date : 2025-06-23 DOI: 10.1007/s00493-025-00162-2
Christos A. Athanasiadis
{"title":"Local h-polynomials, Uniform Triangulations and Real-rootedness","authors":"Christos A. Athanasiadis","doi":"10.1007/s00493-025-00162-2","DOIUrl":"https://doi.org/10.1007/s00493-025-00162-2","url":null,"abstract":"&lt;p&gt;The local &lt;i&gt;h&lt;/i&gt;-polynomial was introduced by Stanley as a fundamental enumerative invariant of a triangulation &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.013ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -778.3 833.5 866.5\" width=\"1.936ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-394\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;Delta&lt;/script&gt;&lt;/span&gt; of a simplex. This polynomial is known to have nonnegative and symmetric coefficients and is conjectured to be &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"1.909ex\" role=\"img\" style=\"vertical-align: -0.705ex;\" viewbox=\"0 -518.7 543.5 822.1\" width=\"1.262ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-3B3\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;gamma&lt;/script&gt;&lt;/span&gt;-positive when &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.009ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -777 833.5 865.1\" width=\"1.936ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-394\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;Delta&lt;/script&gt;&lt;/span&gt; is flag. This paper shows that the local &lt;i&gt;h&lt;/i&gt;-polynomial has the stronger property of being real-rooted when &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"2.013ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -778.3 833.5 866.5\" width=\"1.936ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-394\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;Delta&lt;/script&gt;&lt;/span&gt; is the barycentric subdivision of an arbitrary geometric triangulation &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"&gt;&lt;svg focusable=\"false\" height=\"1.912ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -735.2 625.5 823.4\" width=\"1.453ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-393\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;Gamma&lt;/script&gt;&lt;/span&gt; of the simplex. An analogous result for edgewise subdivisions is proven. The proofs are based on a new combinatorial formula for the local &lt;i&gt;h&lt;/i&gt;-polynomial of &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"51 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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