Combinatorics on Bounded Free Motzkin Paths and its Applications

  • Hyunsoo Cho
  • JiSun Huh
  • Hayan Nam
  • Jaebum Sohn

Abstract

In this paper, we construct a bijection from a set of bounded free Motzkin paths to a set of bounded Motzkin prefixes that induces a bijection from a set of bounded free Dyck paths to a set of bounded Dyck prefixes. We also give bijections between a set of bounded cornerless Motzkin paths and a set of $t$-core partitions, and a set of bounded cornerless symmetric Motzkin paths and a set of self-conjugate $t$-core partitions. As an application, we get explicit formulas for the number of ordinary and self-conjugate $t$ core partitions with a fixed number of corners.

Published
2023-03-24
Article Number
P1.52