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THE LENGTH OF SHORT WORDS IN UNAVOIDABLE SETS

HIGGINS, PETER M (2011) 'THE LENGTH OF SHORT WORDS IN UNAVOIDABLE SETS.' International Journal of Algebra and Computation, 21 (06). pp. 951-960. ISSN 0218-1967

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Abstract

<jats:p> Maximum possible lengths of short words in unavoidable sets of order no more than n have the form log n + O( log log n). The respective log bases of the upper and lower bounds of the shortest and second shortest words are (for a two-letter alphabet) 2 and τ, the Golden Ratio. The latter result comes through identifying certain bases of free monoids. </jats:p>

Item Type: Article
Uncontrolled Keywords: Unavoidable set; free monoid; Fibonacci number; Golden Ratio
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 12 Feb 2013 13:08
Last Modified: 15 Jan 2022 00:29
URI: http://repository.essex.ac.uk/id/eprint/5513

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