author = {G.E. Andrews and P. Paule},
title = {{MacMahon's Partition Analysis XV: Parity}},
language = {english},
abstract = {We apply the methods of partition analysis to partitions in which the parity of parts plays a role. We begin with an in-depth treatment of the generating function for the partitions from the first G ̈ollnitz-Gordon identity. We then deduce a Schmidt-type theorem related to the false theta functions. We also consider: (1) position parity, (2) partitions with distinct even parts, (3) partitions with distinct odd parts. One of the corollaries of these last considerations is a new interpretation of Hei-Chi Chan’s cubic partitions. A second part of our article is devoted to the algorithmic derivation of identities and arithmetic congruences related to the generating functions considered in part one, including cubic partitions. To this end, Smoot’s implementation of Radu’s Ramanujan-Kolberg algorithm is used. Finally, we give a short description which explains how to use the Omega package to derive special instances of the results of part one.},
number = {23-14},
year = {2023},
month = {December},
keywords = {G ̈ollnitz-Gordon partitions, Schmidt-type identities, parity of parts, MacMahon’s partition analysis, q-series, partition congruences, Radu’s Ramanujan-Kolberg algorithm, the Omega package},
length = {31},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}