Student Summer Scholars
 

Generalized Frobenius Partitions with Nonzero Row Difference

Brian Drake, Grand Valley State University
Kelsey A. Scott, Grand Valley State University

This file has been withdrawn by request of the author.

Abstract

Congruences for the partition numbers were first established by Ramanujan in the early twentieth century. Since then, two-rowed arrays called generalized Frobenius partitions have been shown to satisfy the same kinds of congruences. We extend the theory of generalized Frobenius partitions to include arrays whose rows may differ in length and show that the numbers of these objects satisfy analogous congruences.

 

Abstract

Congruences for the partition numbers were first established by Ramanujan in the early twentieth century. Since then, two-rowed arrays called generalized Frobenius partitions have been shown to satisfy the same kinds of congruences. We extend the theory of generalized Frobenius partitions to include arrays whose rows may differ in length and show that the numbers of these objects satisfy analogous congruences.