On some combinatorics of Rogers–Ramanujan type identities using signed color partitions

Abstract

In this work we use combinatorial tools “color partitions,” “split color partitions,” and “signed partitions” notion to define “signed color partitions” that are further used to derive one hundred Rogers–Ramanujan type identities. The paper lists and provides combinatorial argument using signed color partitions of q-identities listed in Chu–Zhang and Slater’s compendium.