Continued fractions and generalized patterns
European Journal of Combinatorics
Pattern frequency sequences and internal zeros
Advances in Applied Mathematics - Special issue: Memory of Rodica Simon
Enumeration of ad-nilpotent b-ideals for simple Lie algebras
Advances in Applied Mathematics - Special issue: Memory of Rodica Simon
On the diagram of 132-avoiding permutations
European Journal of Combinatorics
Bijections for refined restricted permutations
Journal of Combinatorial Theory Series A
132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers
Discrete Applied Mathematics
Decreasing Subsequences in Permutations and Wilf Equivalence for Involutions
Journal of Algebraic Combinatorics: An International Journal
Generalized triangulations and diagonal-free subsets of stack polyominoes
Journal of Combinatorial Theory Series A
Horse paths, restricted 132-avoiding permutations, continued fractions, and Chebyshev polynomials
Discrete Applied Mathematics
Dyck paths and restricted permutations
Discrete Applied Mathematics
Old and young leaves on plane trees
European Journal of Combinatorics
Refined restricted involutions
European Journal of Combinatorics
On bijections for pattern-avoiding permutations
Journal of Combinatorial Theory Series A
Horse paths, restricted 132-avoiding permutations, continued fractions, and Chebyshev polynomials
Discrete Applied Mathematics
The joint distribution of consecutive patterns and descents in permutations avoiding 3-1-2
European Journal of Combinatorics
Counting permutations with no long monotone subsequence via generating trees and the kernel method
Journal of Algebraic Combinatorics: An International Journal
Visits to Level r by Dyck Paths
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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We exhibit a bijection between 132-avoiding permutations and Dyck paths. Using this bijection, it is shown that all the recently discovered results on generating functions for 132-avoiding permutations with a given number of occurrences of the pattern 12...k follow directly from old results on the enumeration of Motzkin paths, among which is a continued fraction result due to Flajolet. As a bonus, we use these observations to derive further results and a precise asymptotic estimate for the number of 132-avoiding permutations of {1,2,...,n} with exactly r occurrences of the pattern 12...k. Second, we exhibit a bijection between 123-avoiding permutations and Dyck paths. When combined with a result of Roblet and Viennot, this bijection allows us to express the generating function for 123-avoiding permutations with a given number of occurrences of the pattern (k-1)(k-2)...1k in the form of a continued fraction and to derive further results for these permutations.