English

New partition identities for odd w odd

Combinatorics 2023-01-31 v1 Number Theory

Abstract

In this note we conjecture Rogers-Ramanujan type colored partition identities for an array with odd number of rows w such that the first and the last row consist of even positive integers. In a strange way this is different from the partition identities for the array with odd number of rows w such that the first and the last row consist of odd positive integers -- the partition identities conjectured by S. Capparelli, A. Meurman, A. Primc and the author and related to standard representations of the affine Lie algebra of type C(1)C^{(1)}_\ell for w=2+1w=2\ell+1. The conjecture is based on numerical evidence.

Keywords

Cite

@article{arxiv.2301.12484,
  title  = {New partition identities for odd w odd},
  author = {Mirko Primc},
  journal= {arXiv preprint arXiv:2301.12484},
  year   = {2023}
}

Comments

7 pages

R2 v1 2026-06-28T08:25:28.815Z