Some remarks about acyclic and tridiagonal Birkhoff polytopes

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• 作者：Du&scaron ; ko Jojić ^{ducci68@teol.net" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05A15 ; 15A51 ; 52B05
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：495
• 期：Complete
• 页码：108-121
• 全文大小：392 K

文摘

For a given tree T   we consider the facial structure of the acyclic Birkhoff polytope class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000501&_mathId=si1.gif&_user=111111111&_pii=S0024379516000501&_rdoc=1&_issn=00243795&md5=4b2772a2332517bc6bc3b706f5659210" title="Click to view the MathML source">Ω(T)class="mathContainer hidden">class="mathCode">$\mathrm{\Omega }(T)$. We also determine the f  -vector of the polytope class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000501&_mathId=si2.gif&_user=111111111&_pii=S0024379516000501&_rdoc=1&_issn=00243795&md5=9f59f534cfc006673651eea00a1dd088">class="imgLazyJSB inlineImage" height="16" width="22" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516000501-si2.gif">class="mathContainer hidden">class="mathCode">${\mathrm{\Omega }}_n^t$ consisting of all tridiagonal doubly stochastic matrices of order n  . Finally, we count the number of combinatorially distinct faces of class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000501&_mathId=si2.gif&_user=111111111&_pii=S0024379516000501&_rdoc=1&_issn=00243795&md5=9f59f534cfc006673651eea00a1dd088">class="imgLazyJSB inlineImage" height="16" width="22" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516000501-si2.gif">class="mathContainer hidden">class="mathCode">${\mathrm{\Omega }}_n^t$ in each dimension.