A bijective proof and generalization of Siladi\'c's Theorem

Abstract

In a recent paper, Dousse introduced a refinement of Siladi\'c's theorem on partitions, where parts occur in two primary and three secondary colors. Her proof used the method of weighted words and $q$-difference equations. The purpose of this paper is to give a bijective proof of a generalization of Dousse's theorem from two primary colors to an arbitrary number of primary colors.