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• W2951540926 abstract "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 cite{Reg1998} for exact asymptotics for the number of words on $k$ letters of length $n$ that avoids the pattern $12...(ell+1)$. Moreover, we give the first combinatorial proof of the exact formula cite{Burstein} for the number of words on $k$ letters of length $n$ avoiding a three letter permutation pattern." @default.
• W2951540926 created "2019-06-27" @default.
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• W2951540926 date "2003-09-17" @default.
• W2951540926 modified "2023-10-05" @default.
• W2951540926 title "Finite automata and pattern avoidance in words" @default.
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