Group Actions on Partitions

Byungchan Kim

Abstract


We introduce group actions on the integer partitions and their variances. Using generating functions and Burnside's lemma, we study arithmetic properties of the counting functions arising from group actions. In particular, we find a modulo 4 congruence involving the number of ordinary partitions and the number of partitions into distinct parts.


Keywords


Partitions; Unimodal sequences; Group action; Partition congruence; Bailey pairs; Bailey Lemma

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