Jaebum Sohn

Affiliation: Yonsei University

Title Of Talk: Corners of $(t, tk \\pm 1)$-Core Partitions and Their Self-Conjugate Analogues

Abstract: The number of corners of a partition equals the number of its distinct parts. Following the work of Huang and Wang, the enumeration of simultaneous core partitions with a fixed number of corners has attracted considerable attention. Huang and Wang enumerated $(t, t+1)$-core and $(t, t+1, t+2)$-core partitions with $m$ corners, and Cho, Huh, and Sohn later generalized this to $(t, t+1, \ldots, t+p)$-core partitions. In this talk, we study $(t, tk \pm 1)$-core partitions with a fixed number of corners. We first derive an explicit formula for the number of such partitions. Furthermore, in the self-conjugate case, we construct a bijection between self-conjugate $(t, tk \pm 1)$-core partitions with a fixed number of corners and certain $(\lfloor t/2 \rfloor + 1)$-tuples satisfying explicit conditions. As a consequence, we obtain an enumeration formula for the self-conjugate case as well.

WARNING: This page contains MATH-JAX

Last update made Tue Mar 10 21:28:06 CDT 2026.
Please report problems to: fgarvan@ufl.edu