Quiver mutation sequences and $q$-binomial identities

TL;DR

This paper introduces a partition function for quiver mutation sequences, expressing it as a ratio of quantum dilogarithms, enabling systematic construction of $q$-binomial identities.

Contribution

It presents a novel partition function for quiver mutations and links it to quantum dilogarithms, facilitating new $q$-binomial identities.

Findings

Partition function expressed as a ratio of quantum dilogarithms

Systematic construction of $q$-binomial multisum identities

Provides a new framework for analyzing quiver mutation sequences

Abstract

In this paper, first we introduce a quantity called a partition function for a quiver mutation sequence. The partition function is a generating function whose weight is a $q$-binomial associated with each mutation. Then, we show that the partition function can be expressed as a ratio of products of quantum dilogarithms. This provides a systematic way of constructing various $q$-binomial multisum identities.