Equivalence classes of Dyck paths modulo some statistics

被引：9
|
作者：
Baril, Jean-Luc [1 ]
Petrossian, Armen [1 ]
机构：
[1] Univ Bourgogne, UMR CNRS 6306 LE2I, F-21078 Dijon, France
来源：
DISCRETE MATHEMATICS | 2015年 / 338卷 / 04期
关键词：
Dyck path; Equivalence relation; Statistics; Rise; Peak; Valley; Catalan; Motzkin and Fibonacci sequences; STRINGS;
D O I：
10.1016/j.disc.2014.12.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate new equivalence relations on the set D of Dyck paths relatively to the three statistics of double rises, peaks and valleys. Two Dyck paths are r-equivalent (respectively p-equivalent and v-equivalent) whenever the positions of their double rises (respectively peaks and valleys) are the same. Then, we provide generating functions for the numbers of r-, p- and v-equivalence classes of D. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：655 / 660
页数：6
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