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
Publication date:
1.8.2016.
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