DOIONLINE 
DOIONLINE Publish In |
International Journal of Advances in Science, Engineering and Technology(IJASEAT)-IJASEAT |
 Journal Home Volume Issue |
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Issue |
Volume-5, Issue-4 ( Oct, 2017 ) | |||||||||
Paper Title |
New Congruences Modulo 3 for 11-Core Partition Function | |||||||||
Author Name |
Utpal Pore, S.N.Fathima | |||||||||
Affilition |
Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry - 605 014, India | |||||||||
Pages |
38-40 | |||||||||
Abstract |
If t is a positive integer, then a partition of a nonnegativeintegern is a t-core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of t. These partitions play important roles in the study of irreducible representations of the symmetric group Sn. Let a(n)denote the number of t-core partitions of n. There are many interesting congruences proved by Granville, Ono, Garvan for the p-core partition functions a(n)where p is a prime. In this paper, we derive new congruences modulo 3 for the 11-core partition function a11(n) by using an identity given by Chan and Toh and a p-dissection of Ramanujan's theta functionf1 due to Cui and Gu. Keywords - Congruences, Dissection, t-core partitions, Theta function. | |||||||||
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