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On the positivity of the number of t-core partitions

Ken Ono — 1994

Acta Arithmetica

A partition of a positive integer n is a nonincreasing sequence of positive integers with sum n . Here we define a special class of partitions. 1. Let t 1 be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partitionof n . The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan’s congruences for the ordinary partition function [3, 4, 6]. If t 1 and n 0 , then we define...

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