Exterior pairs and up step statistics on Dyck paths

Sen Peng Eu, Tung Shan Fu

研究成果: 雜誌貢獻期刊論文同行評審

摘要

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.

原文英語
期刊Electronic Journal of Combinatorics
18
發行號1
DOIs
出版狀態已發佈 - 2011

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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