On the positivity of the number of t-core partitions
Ken Ono
Acta Arithmetica, Tome 68 (1994), p. 221-228 / Harvested from The Polish Digital Mathematics Library
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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. 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 ct(n) to be the number of partitions of n that are t-core partitions. The arithmetic of ct(n) is studied in [3,4]. The power series generating function for ct(n) is given by the infinite product: ∑n=0∞ ct(n)qn= n=1∞

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:206601 
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Ken Ono. On the positivity of the number of t-core partitions. Acta Arithmetica, Tome 68 (1994) pp. 221-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav66i3p221bwm/

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