Geodesic
On the positivity of the number of t-core partitions
Acta Arithmetica, Tome 66 (1994) no. 3, pp. 221-228.

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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. \de{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 partition} of $n.$ \vskip 4pt plus 2pt 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 $c_t(n)$ to be the number of partitions of n that are t-core partitions. The arithmetic of $c_t(n)$ is studied in [3,$\,$4]. The power series generating function for $c_t(n)$ is given by the infinite product: ∑_{n=0}^{∞} c_t(n)q^n= \prod_{n=1}^{∞
DOI : 10.4064/aa-66-3-221-228

Ken Ono 1

1 
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Ken Ono. On the positivity of the number of t-core partitions. Acta Arithmetica, Tome 66 (1994) no. 3, pp. 221-228. doi : 10.4064/aa-66-3-221-228. http://geodesic.mathdoc.fr/articles/10.4064/aa-66-3-221-228/

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