New partition identities for odd w odd

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 $C^{(1)}_\ell$ for $w=2\ell+1$. The conjecture is based on numerical evidence.