A New Matrix-Tree Theorem

dc.creatorMasbaum, Gregor
dc.creatorVaintrob, Arkady
dc.date2001-09-17
dc.date2002-02-28
dc.date.accessioned2026-07-07T04:43:24Z
dc.date.available2026-07-07T04:43:24Z
dc.descriptionThe classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case of three-graphs (that is, hypergraphs whose edges have exactly three vertices) the spanning trees are generated by the Pfaffian of a suitably defined matrix. This result can be interpreted topologically as an expression for the lowest order term of the Alexander-Conway polynomial of an algebraically split link. We also prove some algebraic properties of our Pfaffian-tree polynomial.
dc.descriptionminor changes, 29 pages, version accepted for publication in Int. Math. Res. Notices
dc.identifierhttps://arxiv.org/abs/math/0109104
dc.identifierhttp://arxiv.org/abs/math/0109104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62204
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subject05C50 (Primary); 15A15; 57M27 (Secondary)
dc.titleA New Matrix-Tree Theorem
dc.typetext

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