A New Matrix-Tree Theorem
| dc.creator | Masbaum, Gregor | |
| dc.creator | Vaintrob, Arkady | |
| dc.date | 2001-09-17 | |
| dc.date | 2002-02-28 | |
| dc.date.accessioned | 2026-07-07T04:43:24Z | |
| dc.date.available | 2026-07-07T04:43:24Z | |
| dc.description | The 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.description | minor changes, 29 pages, version accepted for publication in Int. Math. Res. Notices | |
| dc.identifier | https://arxiv.org/abs/math/0109104 | |
| dc.identifier | http://arxiv.org/abs/math/0109104 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62204 | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | Quantum Algebra | |
| dc.subject | 05C50 (Primary); 15A15; 57M27 (Secondary) | |
| dc.title | A New Matrix-Tree Theorem | |
| dc.type | text |