Congruences in ordered pairs of partitions
type: Item
instance of: scholarly article
title: Congruences in ordered pairs of partitions
zbMATH Open document ID: 1063.05016
DOI: 10.1155/S0161171204311439
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/51297
review text: Summary: Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence \(p_{-1} (n)\). The rank has been widely studied as have been other statistics, such as the crank. In this paper a `birank' is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a congruence in \(p_{-2}(n)\).
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 2171612
zbMATH Keywords: statistics
author: Paul S. Hammond
author: Richard P. Lewis
MaRDI profile type: Publication
OpenAlex ID: W2159552098
Recommended article: Q5384289
Recommended article: CONGRUENCES FOR PARTITION PAIRS WITH CONDITIONS
Recommended article: Q5041360
Recommended article: Q5648416
Recommended article: Congruences for a certain partition function
Recommended article: Sequentially congruent partitions and related bijections
Recommended article: Congruences for the number of partitions and bipartitions with distinct even parts
Recommended article: Congruences of the Partition Function
Recommended article: Q4885311
Recommended article: On congruences and partial orders
description: scientific article; zbMATH DE number 2171612