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

TL;DR

This paper provides a bijective proof and generalization of Siladić's theorem, extending Dousse's refinement from two to any number of primary colors in partition theory.

Contribution

It introduces a bijective proof for a generalized version of Dousse's refinement of Siladić's theorem with an arbitrary number of primary colors.

Findings

Established a bijective proof for the generalized theorem.

Extended the refinement to any number of primary colors.

Connected weighted words and $q$-difference equations to combinatorial proofs.

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.