Signed Counting on Restricted Partitions and Combinatorial Proofs of Three Identities

Shishuo Fu; Chenwei Wang

Signed Counting on Restricted Partitions and Combinatorial Proofs of Three Identities

Combinatorics 2026-07-19 v1

Authors: Shishuo Fu , Chenwei Wang

Abstract

Signed enumerations of l-regular partitions by the parity of the number of parts are known to correspond to partitions with congruence conditions. Inspired by the recent combinatorial approaches of Ballantine-Merca and Liu for such identities, we provide combinatorial proofs of three identities for l-regular partitions and their variants. Two of these were originally established analytically by Hickerson and Robbins, respectively.

Keywords

signed enumeration l-regular partitions combinatorial proofs partition identities congruence conditions

Cite

@article{arxiv.2607.17296,
  title  = {Signed Counting on Restricted Partitions and Combinatorial Proofs of Three Identities},
  author = {Shishuo Fu and Chenwei Wang},
  journal= {arXiv preprint arXiv:2607.17296},
  year   = {2026}
}

Comments

16pages