UC Berkeley

A configuration of the twenty vertex model is an orientation of each edge in a triangular lattice such that at each vertex the number of incoming and outgoing edges is equal. This is similar to the six vertex model, which takes place on a square lattice, that has long been of interest to combinatorialists for its connections to alternating sign matrices. Recently Di Francesco and Guitter uncovered interesting combinatorics for the twenty vertex model which previously was primarily studied by physicists. Di Francesco was also able to relate configurations of the twenty vertex model to domino tilings of a so-called Aztec triangle, and conjectured a product formula for enumerating these configurations. We examine the enumeration of these objects including several combinatorial bijections of the twenty vertex model. In particular we establish a relation from the aforementioned domino tilings to sequences of partitions, and then introduce a generalized Aztec triangle for which we obtain a generalization to Di Francesco's conjecture.