Counting Partitions on the Abacus

Details Counting Partitions on the Abacus Counting Partitions on the Abacus

2006-09-06

arxiv.org/abs/math/0609175v1

Mathematics

Combinatorics

11 pages, 1 figure

Scientific paper

In 2003, Maroti showed that one could use the machinery of l-cores and l-quotients of partitions to establish lower bounds for p(n), the number of partitions of n. In this paper we explore these ideas in the case l=2, using them to give a largely combinatorial proof of an effective upper bound on p(n), and to prove asymptotic formulae for the number of self-conjugate partitions, and the number of partitions with distinct parts. In a further application we give a combinatorial proof of an identity originally due to Gauss.

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