Perfect matching

We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on a weighted, bipartite, doubly periodic graph G embedded in the plane. We derive explicit formulas for the surface tension and local Gibbs measure probabilities of these models. The answers involve a certain plane algebraic curve, which is the spectral curve of the Kasteleyn operator of the graph. For example, the surface tension is the Legendre dual of the Ronkin function of the spectral curve. The amoeba of the spectral curve represents the phase diagram of the dimer model.

39p noel_noel 17-01-2013 51 7   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Perfect Matchings in Claw-free Cubic Graphs...

6p thulanh7 05-10-2011 44 1   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Enumeration of perfect matchings of a type of quadratic lattice on the torus...

14p thulanh7 04-10-2011 47 4   Download

In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

13p thulanh8 19-09-2011 68 4   Download

In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

37p thulanh8 19-09-2011 58 14   Download

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Pfaffian orientation and enumeration of perfect matchings for some Cartesian products of graphs...

11p thulanh8 17-09-2011 47 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: The maximum number of perfect matchings in graphs with a given degree sequence...

2p thulanh6 15-09-2011 62 3   Download

A subset M  E(G) of the edge set E(G) of a graph G is called a matching provided that no two edges in M have a vertex in common. A perfect matching M is a matching with the property that each vertex of G is incident with an edge in M. For k a positive integer, a graph G is k-extendable provided that G has a matching of size k and every matching in G of size at most k can be extended to a perfect matching in G.

15p thulanh6 14-09-2011 57 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học hay nhất của tạp chí toán học quốc tế đề tài: On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs...

11p thulanh4 11-09-2011 70 4   Download

Tuyển tập các báo cáo nghiên cứu khoa học hay nhất của tạp chí toán học quốc tế đề tài: Perfect matchings in -regular graphs...

4p thulanh4 11-09-2011 42 3   Download

Cleavage is a low-energy fracture that propagates along well-defined low-index crystallographic planes known as cleavage planes. Theoretically, a cleavage fracture should have perfectly matching faces and should be completely flat and featureless. However, engineering alloys are polycrystalline and contain grain and subgrain boundaries, inclusions, dislocations, and other imperfections that affect a propagating cleavage fracture so that true, featureless cleavage is seldom observed.

10p lyacau 28-12-2009 81 5   Download