ELECTRONIC JOURNAL OF COMBINATORICS vol. 30, no. 1
Publisher
ELECTRONIC JOURNAL OF COMBINATORICS
Indexed
SCIE; SCOPUS
Document Type
Article
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.