Corners of Self-Conjugate $(t,tk\pm 1)$-Core Partitions

Abstract

A corner of a partition is a removable box in the Young diagram. Initiated by Huang and Wang, there has been research on the number of simultaneous core partitions with a fixed number of corners. In this paper, we give a bijection between the set of self-conjugate $(t,tk\pm 1)$-core partitions with a fixed number of corners and the set of $(\lfloor t/2 \rfloor +1)$-tuples with certain conditions. As a result of this bijection, we count the number of such partitions.