Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
Generating trees and forbidden subsequences
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
Forbidden subsequences and Chebyshev polynomials
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
Regular Article: Restricted 132-Avoiding Permutations
Advances in Applied Mathematics
Permutations with Restricted Patterns and Dyck Paths
Advances in Applied Mathematics
Continued fractions and generalized patterns
European Journal of Combinatorics
Multi-avoidance of generalised patterns
Discrete Mathematics
Consecutive patterns in permutations
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Introduction to partially ordered patterns
Discrete Applied Mathematics
| Hi-index | 0.04 |
Several authors have examined connections among 132-avoiding permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we find analogues for some of these results for permutations π avoiding 132 and 1□23 (there is no occurrence πi j j+1 such that 1 ≤i ≤j - 2) and provide a combinatorial interpretation for such permutations in terms of lattice paths. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid both 132 and 1□23, and certain additional patterns. We also give generating functions for permutations avoiding 132 and 1□23 and containing certain additional patterns exactly once. In all cases we express these generating functions in terms of Chebyshev polynomials of the second kind.