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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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204311439 |
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| author | Paul Hammond Richard Lewis |
| author_facet | Paul Hammond Richard Lewis |
| author_sort | Paul Hammond |
| collection | DOAJ |
| 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). |
| format | Article |
| id | doaj-art-130c80eedd474d639aaf0b9ffb84f4ba |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-130c80eedd474d639aaf0b9ffb84f4ba2025-02-03T01:02:12ZengWileyInternational 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 |
| spellingShingle | Paul Hammond Richard Lewis Congruences in ordered pairs of partitions International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Congruences in ordered pairs of partitions |
| title_sort | congruences in ordered pairs of partitions |
| url | http://dx.doi.org/10.1155/S0161171204311439 |
| work_keys_str_mv | AT paulhammond congruencesinorderedpairsofpartitions AT richardlewis congruencesinorderedpairsofpartitions |