International Journal of Advances in Science, Engineering and Technology(IJASEAT)
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Volume-7, Issue-1, Spl. Iss-1  ( Feb, 2019 )
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Paper Title
New Congruences Modulo 3 for 11-Core Partition Function

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.


Author - Utpal Pore, S.N.Fathima

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| Published on 2018-01-03
   
   
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