Diagonal Hooks and a Schmidt-Type Partition Identity

Abstract

In a recent paper of Andrews and Paule, several Schmidt-type partition identities are considered within the framework of MacMahon's Partition Analysis. Following their work, we derive a new Schmidt-type identity concerning diagonal hooks of partitions. We provide an analytic proof based on MacMahon's Partition Analysis and a combinatorial proof through an involution on the set of partitions. We also establish connections between Schmidt-type distinct partitions and partitions with nonpositive and negative cranks.