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 |
|---|---|
| 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: | 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: | 18 Aug 2022 11:01 |
| URI: | http://repository.essex.ac.uk/id/eprint/5513 |