Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
Enumerative combinatorics
The solution of a conjecture of Stanley and Wilf for all layered patterns
Journal of Combinatorial Theory Series A
On the number of permutations avoiding a given pattern
Journal of Combinatorial Theory Series A
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Generating functions for generating trees
Discrete Mathematics
Discrete Mathematics - Kleitman and combinatorics: a celebration
Restricted k-ary words and functional equations
Discrete Applied Mathematics
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We say that a word w on a totally ordered alphabet avoids the word v if there are no subsequences in w order-equivalent to v. In this paper we suggest a new approach to the enumeration of words on at most k letters avoiding a given pattern. By studying an automaton which for fixed k generates the words avoiding a given pattern we derive several previously known results for these kind of problems, as well as many new. In particular, we give a simple proof of the formula (Electron. J. Combin. 5(1998) #R15) for exact asymptotics for the number of words on k letters of length n that avoids the pattern 12...(l + 1). Moreover, we give the first combinatorial proof of the exact formula (Enumeration of words with forbidden patterns, Ph.D. Thesis, University of Pennsylvania, 1998) for the number of words on k letters of length n avoiding a three letter permutation pattern.