TL;DR
This paper demonstrates that all avoidable patterns of length up to n can be avoided using an alphabet with 2(n+2) letters, providing a bound on alphabet size for pattern avoidance.
Contribution
It establishes a new upper bound on the alphabet size needed to avoid all patterns of length up to n.
Findings
All avoidable patterns of length ≤ n can be avoided with 2(n+2) letters.
Provides a constructive bound for pattern avoidance.
Advances understanding of pattern avoidance in combinatorics.
Abstract
The set of all avoidable patterns in n or fewer letters can be avoided on an alphabet with 2(n+2) letters.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Cellular Automata and Applications