Some considerations on Hydra groups and a new bound for the length of words
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After a survey on some recent results of Riley and others on Ackermann functions and Hydra groups, we make an analogy between DNA sequences, whose growth is the same of that of Hydra groups, and a musical piece, written with the same algorithmic criterion. This is mainly an aesthetic observation, which emphasizes the importance of the combinatorics of words in two different contexts. A result of specific mathematical interest is placed at the end, where we sharpen some previous bounds on deterministic finite automata in which there are languages with hairpins.
Keywordsisoperimetric functions finitely presented groups lengths of words counterpoint Myhill-Nerode’s theorem
2010 Mathematics Subject ClassificationPrimary 57M50 Secondary 68R05, 68Q15
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