Exterior pairs and up step statistics on Dyck paths

Sen Peng Eu; Tung Shan Fu

doi:10.37236/579

Exterior pairs and up step statistics on Dyck paths

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

摘要

Let C_n be the set of Dyck paths of length n. In this paper, by a new auto- morphism of ordered trees, we prove that the statistic 'number of exterior pairs', introduced by A. Denise and R. Simion, on the set C_n is equidistributed with the statistic 'number of up steps at height h with h ≡ 0 (mod 3)'. Moreover, for m ≥ 3, we prove that the two statistics 'number of up steps at height h with h ≡ 0 (mod m)' and 'number of up steps at height h with h ≡ m - 1 (mod m)' on the set C_n are 'almost equidistributed'. Both results are proved combinatorially.

原文	英語
期刊	Electronic Journal of Combinatorics
卷	18
發行號	1
DOIs	https://doi.org/10.37236/579
出版狀態	已發佈 - 2011
對外發佈	是

ASJC Scopus subject areas

理論電腦科學
幾何和拓撲
離散數學和組合
計算機理論與數學
應用數學

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AB - Let Cn be the set of Dyck paths of length n. In this paper, by a new auto- morphism of ordered trees, we prove that the statistic 'number of exterior pairs', introduced by A. Denise and R. Simion, on the set Cn is equidistributed with the statistic 'number of up steps at height h with h ≡ 0 (mod 3)'. Moreover, for m ≥ 3, we prove that the two statistics 'number of up steps at height h with h ≡ 0 (mod m)' and 'number of up steps at height h with h ≡ m - 1 (mod m)' on the set Cn are 'almost equidistributed'. Both results are proved combinatorially.

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KW - Ordered tree

KW - Planted tree

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Exterior pairs and up step statistics on Dyck paths

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