Abstract
Separating words with automata is a longstanding open problem in combinatorics on words. In this paper we present a related algebraic problem. What is the minimal length of a nontrivial identical relation in the symmetric group S n ?
Our main contribution is an upper bound \(2^{O(\sqrt n\log n)}\) on the length of the shortest nontrivial identical relation in S n . We also give lower bounds for words of a special types. These bounds can be applied to the problem of separating words by reversible automata. In this way we obtain an another proof of the Robson’s square root bound.
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Gimadeev, R.A., Vyalyi, M.N. (2010). Identical Relations in Symmetric Groups and Separating Words with Reversible Automata. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_14
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DOI: https://doi.org/10.1007/978-3-642-13182-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13181-3
Online ISBN: 978-3-642-13182-0
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