# Combinatorics of Ramanujan--Slater type identities

## TL;DR

This paper completes a family of four Ramanujan-Slater type q-series identities related to modulus 36, explores their combinatorial implications, and connects them to previous identities studied in related moduli.

## Contribution

It introduces the missing identity in the family and analyzes its combinatorial significance, expanding understanding of these special q-series identities.

## Key findings

- Identifies the missing q-series identity for modulus 36
- Explores combinatorial implications of the identities
- Connects new identities to previous work on moduli 18 and 24

## Abstract

We provide the missing member of a family of four $q$-series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered in "Identities of the Ramanujan-Slater type related to the moduli 18 and 24," [\emph{J. Math. Anal. Appl.} \textbf{344}/2 (2008) 765--777].