PED and POD partitions: Combinatorial proofs of recurrence relations

PED partitions are with even parts distinct while odd unrestricted. Similarly, POD have In [16] several recurrence relations for the number of n proved analytically. They similar to relation given by Euler's pentagonal theorem. We provide combinatorial proofs all these theorems and also theorem analytically in [11], which motivated [16]. Moreover, we prove combinatorially a [7], Beck-type identities involving partitions, other results about partitions.