Séminaire Lotharingien de Combinatoire, 84B.35 (2020), 12 pp.
Hyunsoo Cho, Jisun Huh and Jaebum Sohn
The (s,s+d,...,s+pd)-Core Partitions and Rational Motzkin Paths
Abstract.
In this article, we propose an (s+d,d)-abacus for
(s,s+d,...,s+pd)-core partitions and establish a bijection between
(s,s+d,...,s+pd)-core partitions and rational Motzkin paths of
type (s+d,-d). This result not only gives a lattice path
interpretation of the (s,s+d,...,s+pd)-core partitions but also
counts them with a closed formula. Also we enumerate
(s,s+1,...,s+p)-core partitions with k corners and
self-conjugate (s,s+1,...,s+p)-core partitions.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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