Name
Abstract | ||
|---|---|---|
The symmetric q; t-Catalan polynomial Cn(q; t), which specializes to the Catalan polynomial Cn(q )w hent = 1, was dened by Garsia and Haiman in 1994. In 2000, Garsia and Haglund described statistics a( )a ndb() on Dyck paths such that Cn(q; t )= P q a()tb() where the sum is over all n n Dyck paths. Specializing t = 1 gives the Catalan polynomial Cn(q) dened by Carlitz and Riordan and further studied by Carlitz. Specializing both t =1 andq = 1 gives the usual Catalan number Cn. The Catalan number Cn is known to count the number of n n Dyck paths and the number of 312-avoiding permutations in Sn ,a s well as at least 64 other combinatorial objects. In this paper, we dene a bijection between Dyck paths and 312-avoiding permutations which takes the area statistic a( )o n Dyck paths to the inversion statistic on 312-avoiding permutations. The inversion statistic can be thought of as the number of (21) patterns in a permutation .W e give a characterization for the number of (321), (4321), ::: ,( k 21) patterns that occur in in terms of the corresponding Dyck path. |
Year | Venue | Keywords |
|---|---|---|
2001 | The Electronic Journal of Combinatorics | catalan number |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Bijection,Polynomial,Permutation,Catalan number,Mathematics | Journal | 8 |
Issue | Citations | PageRank |
1 | 11 | 1.11 |
References | Authors | |
4 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jason Bandlow | 1 | 25 | 4.10 |
| Kendra Killpatrick | 2 | 23 | 6.94 |