Validations of the Asymptotic Matching Conjectures
| dc.creator | Friedland, Shmuel | |
| dc.creator | Krop, Elliot | |
| dc.creator | Lundow, Per Hakan | |
| dc.creator | Markström, Klas | |
| dc.date | 2006-02-28 | |
| dc.date | 2008-04-11 | |
| dc.date.accessioned | 2026-07-07T09:31:38Z | |
| dc.date.available | 2026-07-07T09:31:38Z | |
| dc.description | In this paper we review the asymptotic matching conjectures for $r$-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in $d$-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of $r$-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density $p$, for any $p\in [0,1]$, for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite $r$-regular bipartite graphs. | |
| dc.description | 25 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/math/0603001 | |
| dc.identifier | http://arxiv.org/abs/math/0603001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158527 | |
| dc.subject | Combinatorics | |
| dc.subject | Mathematical Physics | |
| dc.subject | 05A15, 05A16, 05C70, 05C80, 82B20 | |
| dc.title | Validations of the Asymptotic Matching Conjectures | |
| dc.type | text |