Double-dimer pairings and skew Young diagrams

Details Double-dimer pairings and skew Young diagrams Double-dimer pairings and skew Young diagrams

2010-07-12

arxiv.org/abs/1007.2006v2

Mathematics

Combinatorics

22 pages, 31 figures

Scientific paper

We study the number of tilings of skew Young diagrams by ribbon tiles shaped like Dyck paths, in which the tiles are "vertically decreasing". We use these quantities to compute pairing probabilities in the double-dimer model: Given a planar bipartite graph $G$ with special vertices, called nodes, on the outer face, the double-dimer model is formed by the superposition of a uniformly random dimer configuration (perfect matching) of $G$ together with a random dimer configuration of the graph formed from $G$ by deleting the nodes. The double-dimer configuration consists of loops, doubled edges, and chains that start and end at the boundary nodes. We are interested in how the chains connect the nodes. An interesting special case is when the graph is $\epsilon(\Z\times\N)$ and the nodes are at evenly spaced locations on the boundary $\R$ as the grid spacing $\epsilon\to 0$.

Affiliated with

Also associated with

No associations

Rating

Double-dimer pairings and skew Young diagrams does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Double-dimer pairings and skew Young diagrams, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Double-dimer pairings and skew Young diagrams will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-350195