Partition identities arising from involutions

Copyright © 2003 Combinatorial Mathematics Society of Australasia (Inc.)Open Access journalWe give a simple combinatorial proof of three identities of Warnaar. The proofs exploit involutions due to Franklin and Schur

Two truncated identities of Gauss

Two new expansions for partial sums of Gauss' triangular and square numbers series are given. As a consequence, we derive a family of inequalities for the overpartition function $\bar{p}(n)$ and for the partition function $p_1(n)$ counting the partitions of $n$ with distinct odd parts. Some further inequalities for variations of partition function are proposed as conjectures.Comment: 9 pages, final versio

Partition identities arising from involutions

We give a simple combinatorial proof of three identities of Warnaar. The proofs exploit involutions due to Franklin and Schur.