Professional paper

On the Euler's Partition Theorem

Ivica Martinjak ; Prirodoslovno-matematički fakultet, Sveučilište u Zagrebu

Abstract

In this paper, we present the Euler's partition theorem, which states that for every natural number the number of odd partitions is equal to the number of strict partitions. First, we prove this theorem bijectively and then using generating functions. We present two Sylvester's bijections which, besides proving Euler's theorem, also give a few other refinements. Fine's theorem is illustrated by using
Dyson's bijection iteratively on concrete examples.

Keywords

integer partition; Euler's theorem; rank of a partition; bijection; generating function; Sylvester's bijection; Dyson's bijection

Hrčak ID:

164848

URI

https://hrcak.srce.hr/164848

Publication date:

1.8.2016.

Article data in other languages: croatian

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