On mex-related partition functions of Andrews and Newman

On partition functions of Andrews and Stanley

G. E. Andrews has established a refinement of the generating function for partitions π according to the numbers O(π) and O(π′) of odd parts in π and the conjugate of π, respectively. In this paper, we derive a refined generating function for partitions into at most M parts less than or equal to N , which is a finite case of Andrew’s refinement.

A Combinatorial Proof of Andrews’ Partition Functions Related to Schur’s Partition Theorem

We construct an involution to show equality between partition functions related to Schur’s second partition theorem.

Andrews Style Partition Identities

We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews’ results in [5]. The novelty is that the method constructs solutions to functional equations which are satisfied by the generating functions. In contrast, the conventional approach is to show that a variant of well-known series satisfies the system ...

Proof of Andrews' Conjecture on Partition Identities

The Andrews–Sellers family of partition congruences

In 1994, James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. In 2002 Dennis Eichhorn and Sellers were able to settle the conjecture for powers up to 4. In this article, we prove Sellers' conjecture for all powers of 5. In addition, we discuss why the Andrews-Sel...