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.
Bibliographical noteFunding 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