Colored Vertex Models and Interacting Reverse Plane Partitions

TL;DR

This paper introduces a novel integrable colored vertex model to study interacting reverse plane partitions, providing a method to compute their generating functions and establishing bijections with single partitions.

Contribution

It presents a new colored vertex model linked to reverse plane partitions and uses the Yang-Baxter equation to analyze their interactions and generating functions.

Findings

Established a bijection with a Yang-Baxter integrable colored vertex model.

Derived the generating function for interacting pairs of reverse plane partitions.

Connected the non-interacting case to single reverse plane partitions.

Abstract

We study the coupling of pairs of reverse plane partitions of the same shape by assigning a certain local interaction between the reverse plane partitions. We show that they are in bijection with a certain Yang-Baxter integrable colored vertex model. By utilizing the Yang-Baxter equation for this colored vertex model, we are able to compute the generating function for the interacting pairs of reverse plane partitions. We also give a bijection between the coupled pairs of reverse plane partitions with the interaction strength set to zero and a single reverse plane partition of the same shape.