Congruences for Generalized Frobenius Partitions of Nonzero Row Difference

TL;DR

This paper extends a counting principle for generalized Frobenius partitions to arrays with nonzero row differences and establishes related congruences, broadening the understanding of partition structures.

Contribution

It introduces a new extension of the counting principle to arrays with nonzero row differences and derives new congruences for these arrays.

Findings

Established new congruences for generalized Frobenius partitions with nonzero row difference.

Extended existing counting principles to a broader class of partition arrays.

Provided theoretical foundations for future research in partition congruences.

Abstract

We extend George Andrew's general principle for counting generalized Frobenius partitions to include arrays with nonzero row difference and establish some congruences for these arrays.