曲阜师范大学学报（自然科学版）2025，Vol.51Issue(4)：29-37,9.DOI:10.3969/j.issn.1001-5337.2025.4.029
广义Narayana数的组合解释
Combinatorial interpretations of the generalized Narayana numbers
摘要
Abstract
Let m,n,k be integers and m ≥0,n≥m+1,1≤k≤n-m.Callan defined the generalized Narayana numbers as Nm(n,k)=m+1/n+1(n+1k)(n-m-1k-1).In this paper,the combinatorial interpretations of the generalized Narayana numbers in the m-Dyck paths,valid strings,standard Young tables,planar trees and complete binary trees are studied.Firstly,the combi-natorial interpretation of the generalized Narayana numbers in the m-Dyck paths is obtained.Then bijec-tions between the m-Dyck paths and the valid strings,standard Young tables,and complete binary trees,are estabilshed,respectively.Finally,the combinatorial interpretations of the generalized Narayana numbers in the above four combinatorial objects is showed.关键词
广义Narayana数/双射/m-Dyck路Key words
generalized Narayana numbers/bijection/m-Dyck path分类
数理科学引用本文复制引用
冯余慧,刘丽..广义Narayana数的组合解释[J].曲阜师范大学学报（自然科学版）,2025,51(4):29-37,9.基金项目
国家自然科学基金(11871304) （11871304）
山东省泰山学者青年专家基金(tsqn202103060). （tsqn202103060）
