n-Color partitions with weighted differences equal to minus two
In this paper we study those n-color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to −2 Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129700104X |
| Summary: | In this paper we study those n-color partitions of Agarwal and Andrews, 1987, in which
each pair of parts has weighted difference equal to −2 Results obtained in this paper for these
partitions include several combinatorial identities, recurrence relations, generating functions, relationships
with the divisor function and computer produced tables. By using these partitions an explicit expression
for the sum of the divisors of odd integers is given. It is shown how these partitions arise in the study of
conjugate and self-conjugate n-color partitions. A combinatorial identity for self-conjugate n-color
partitions is also obtained. We conclude by posing several open problems in the last section. |
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| ISSN: | 0161-1712 1687-0425 |