The Method of Multiple Combinatorial Telescoping

TL;DR

This paper extends the combinatorial telescoping method to handle multiple summations and demonstrates its effectiveness through proofs of identities related to partition parity indices.

Contribution

It introduces a generalized combinatorial telescoping approach applicable to multiple summations, expanding the toolkit for combinatorial proofs.

Findings

Provided combinatorial proofs for Andrews' identities on parity indices of partitions

Generalized telescoping method applicable to complex multiple sums

Enhanced understanding of partition identities through combinatorial techniques

Abstract

We generalize the method of combinatorial telescoping to the case of multiple summations. We shall demonstrate this idea by giving combinatorial proofs for two identities of Andrews on parity indices of partitions.