A Combinatorial Proof of Bass's Evaluations of the Ihara-Selberg Zeta Function for Graphs

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dc.creatorFoata, Dominique
dc.creatorZeilberger, Doron
dc.date1998-06-08
dc.date.accessioned2026-07-07T05:24:57Z
dc.date.available2026-07-07T05:24:57Z
dc.descriptionWe derive combinatorial proofs of the main two evaluations of the Ihara-Selberg Zeta function associated with a graph. We give three proofs of the first evaluation all based on the algebra of Lyndon words. In the third proof it is shown that the first evaluation is an immediate consequence of Amitsur's identity on the characteristic polynomial of a sum of matrices. The second evaluation of the Ihara-Selberg Zeta function is first derived by means of a sign-changing involution technique. Our second approach makes use of a short matrix-algebra argument.
dc.descriptionAMSTeX, to appear in Trans. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/9806037
dc.identifierhttp://arxiv.org/abs/math/9806037
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77012
dc.subjectCombinatorics
dc.titleA Combinatorial Proof of Bass's Evaluations of the Ihara-Selberg Zeta Function for Graphs
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