Congruences in ordered pairs of partitions

Congruences in ordered pairs of partitions

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...

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Main Authors: Paul Hammond, Richard Lewis
Format: Article
Language:English
Published: Hindawi Limited 2004-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171204311439
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spelling doaj-130c80eedd474d639aaf0b9ffb84f4ba2020-11-24T23:23:09ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004472509251210.1155/S0161171204311439Congruences in ordered pairs of partitionsPaul Hammond0Richard Lewis1Department of mathematics, University of Sussex, Falmer, Brighton BN1 9RF, UKDepartment of Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UKDyson 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).http://dx.doi.org/10.1155/S0161171204311439
collection DOAJ
language English
format Article
sources DOAJ
author Paul Hammond
Richard Lewis
spellingShingle Paul Hammond
Richard Lewis
Congruences in ordered pairs of partitions
International Journal of Mathematics and Mathematical Sciences
author_facet Paul Hammond
Richard Lewis
author_sort Paul Hammond
title Congruences in ordered pairs of partitions
title_short Congruences in ordered pairs of partitions
title_full Congruences in ordered pairs of partitions
title_fullStr Congruences in ordered pairs of partitions
title_full_unstemmed Congruences in ordered pairs of partitions
title_sort congruences in ordered pairs of partitions
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2004-01-01
description 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).
url http://dx.doi.org/10.1155/S0161171204311439
work_keys_str_mv AT paulhammond congruencesinorderedpairsofpartitions
AT richardlewis congruencesinorderedpairsofpartitions
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