Dyck paths and restricted permutations

Toufik Mansour, Eva Y.P. Deng, Rosena R.X. Du

Research output: Contribution to journalArticlepeer-review


This paper is devoted to characterize permutations with forbidden patterns by using canonical reduced decompositions, which leads to bijections between Dyck paths and Sn ( 321 ) and Sn ( 231 ), respectively. We also discuss permutations in Sn avoiding two patterns, one of length 3 and the other of length k. These permutations produce a kind of discrete continuity between the Motzkin and the Catalan numbers.

Original languageEnglish
Pages (from-to)1593-1605
Number of pages13
JournalDiscrete Applied Mathematics
Issue number11
StatePublished - 1 Jul 2006

Bibliographical note

Funding Information:
This work was done under the auspices of the 973 Project on Mathematical Mechanization of the Ministry of Science and Technology, and the National Science Foundation of China.


  • Canonical reduced decomposition
  • Dyck path
  • Restricted permutation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Dyck paths and restricted permutations'. Together they form a unique fingerprint.

Cite this