A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
Regular Article: The Enumeration of Permutations with a Prescribed Number of 驴Forbidden驴 Patterns
Advances in Applied Mathematics
Exact enumeration of 1342-avoiding permutations: a close link with labeled trees and planar maps
Journal of Combinatorial Theory Series A
Discrete Mathematics
On the number of permutations avoiding a given pattern
Journal of Combinatorial Theory Series A
Regular Article: Restricted 132-Avoiding Permutations
Advances in Applied Mathematics
Generating functions for generating trees
Discrete Mathematics
Counting Occurrences of 132 in a Permutation
Advances in Applied Mathematics
Excluded permutation matrices and the Stanley-Wilf conjecture
Journal of Combinatorial Theory Series A
Finite automata and pattern avoidance in words
Journal of Combinatorial Theory Series A
Enumeration schemes for restricted permutations
Combinatorics, Probability and Computing
Criteria for the matrix equivalence of words
Theoretical Computer Science
Enumeration of some classes of words avoiding two generalized patterns of length three
Journal of Automata, Languages and Combinatorics
Hi-index | 0.05 |
We present an algorithm for finding a system of recurrence relations for the number of k-ary words of length n that satisfy a certain set of conditions. A rewriting of these relations automatically gives a system of functional equations satisfied by the multivariate generating function that counts k-ary words by their length and the indices of the corresponding recurrence relations. We propose an approach to describing such equations. In several interesting cases the algorithm recovers and refines results on @t-avoiding k-ary words and k-ary words containing @t exactly once, where @t is either a classical, a generalized, or a distanced pattern of length three.