On zeros of the characteristic polynomial of matroids of bounded tree-width

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• 作者：Carolyn Chun^c ; ^{chun@usna.edu" class="auth_mail" title="E-mail the corresponding author} ; Rhiannon Hall^a ; ^{rhiannon.hall@brunel.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Criel Merino^b ; ¹ ; ^{merino@matem.unam.mx" class="auth_mail" title="E-mail the corresponding author} ; Steven Noble^d ; ^{s.noble@bbk.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 刊名：European Journal of Combinatorics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：60
• 期：Complete
• 页码：10-20
• 全文大小：417 K

文摘

We develop some basic tools to work with representable matroids of bounded tree-width and use them to prove that, for any prime power class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300701&_mathId=si2.gif&_user=111111111&_pii=S0195669816300701&_rdoc=1&_issn=01956698&md5=500f4f1d4b70279d29e69ea585267d30" title="Click to view the MathML source">qclass="mathContainer hidden">class="mathCode">$q$ and constant class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300701&_mathId=si3.gif&_user=111111111&_pii=S0195669816300701&_rdoc=1&_issn=01956698&md5=b335fbcefa9c34c0d6e41e8a26f667e4" title="Click to view the MathML source">kclass="mathContainer hidden">class="mathCode">$k$, the characteristic polynomial of any loopless, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300701&_mathId=si4.gif&_user=111111111&_pii=S0195669816300701&_rdoc=1&_issn=01956698&md5=463f85249ecef21aa5bc44ae88b93bbe" title="Click to view the MathML source">GF(q)class="mathContainer hidden">class="mathCode">$GF\left(q\right)$-representable matroid with tree-width class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300701&_mathId=si3.gif&_user=111111111&_pii=S0195669816300701&_rdoc=1&_issn=01956698&md5=b335fbcefa9c34c0d6e41e8a26f667e4" title="Click to view the MathML source">kclass="mathContainer hidden">class="mathCode">$k$ has no real zero greater than class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300701&_mathId=si6.gif&_user=111111111&_pii=S0195669816300701&_rdoc=1&_issn=01956698&md5=b2be0f04d393cdfcf379c76b4e8bcd2c" title="Click to view the MathML source">q^k−1class="mathContainer hidden">class="mathCode">$q^{k-1}$.