HIGGINS, PETER M (2011) THE LENGTH OF SHORT WORDS IN UNAVOIDABLE SETS. International Journal of Algebra and Computation, 21 (06). pp. 951-960. DOI https://doi.org/10.1142/s0218196711006522
HIGGINS, PETER M (2011) THE LENGTH OF SHORT WORDS IN UNAVOIDABLE SETS. International Journal of Algebra and Computation, 21 (06). pp. 951-960. DOI https://doi.org/10.1142/s0218196711006522
HIGGINS, PETER M (2011) THE LENGTH OF SHORT WORDS IN UNAVOIDABLE SETS. International Journal of Algebra and Computation, 21 (06). pp. 951-960. DOI https://doi.org/10.1142/s0218196711006522
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 |
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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 > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 12 Feb 2013 13:08 |
Last Modified: | 30 Oct 2024 19:47 |
URI: | http://repository.essex.ac.uk/id/eprint/5513 |