The (s, s plus d, ..., s plus pd)-core partitions and the rational Motzkin paths

被引：7

作者：

Cho, Hyunsoo ^{[1
]}

Huh, JiSun ^{[2
]}

Sohn, Jaebum ^{[3
]}

机构：

[1] Ewha Womans Univ, Inst Math Sci, Seoul 03760, South Korea

[2] Ajou Univ, Dept Math, Suwon 16499, South Korea

[3] Yonsei Univ, Dept Math, Seoul 03722, South Korea

来源：

ADVANCES IN APPLIED MATHEMATICS | 2020年 / 121卷

基金：

新加坡国家研究基金会;

关键词：

Simultaneous core partitions; Self-conjugate; Corners; Rational Motzkin paths; Generalized Dyck paths; CORE;

D O I：

10.1016/j.aam.2020.102096

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose an (s + d, d)-abacus for (s, s + d, ..., s + pd)-core partitions and establish a bijection between the (s, s + d, ..., s + pd)-core partitions and the 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 an explicit formula. Also we enumerate (s, s + 1, ..., s + p)-core partitions with k corners and self-conjugate ( s, s + 1, ..., s + p)-core partitions. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：17

共 20 条

[1] Multi-cores, posets, and lattice paths [J].