On the entropy and letter frequencies of ternary square-free words

Richard C, Grimm U (2004)

Publication Type: Journal article

Publication year: 2004

Journal

Electronic Journal of Combinatorics The Electronic Journal of Combinatorics

Publisher: The Electronic Journal of Combinatorics

Book Volume: 11

Pages Range: Research Paper 14, 19 pp. (electronic)

Journal Issue: 1

URI: http://www.combinatorics.org/Volume_11/Abstracts/v11i1r14.html

Abstract

We enumerate ternary length- $ℓ$ square-free words, which are words avoiding squares of all words up to length $ℓ$ , for $ℓ \leq 24$ . We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary square-free words. We then consider ternary square-free words with fixed letter densities, thereby proving exponential growth for certain ensembles with various letter densities. We derive consequences for the free energy and entropy of ternary square-free words.

Authors with CRIS profile

Christoph Richard Lehrstuhl für Mathematische Stochastik

Involved external institutions

Open University (OU)

United Kingdom (GB)

How to cite

APA:

Richard, C., & Grimm, U. (2004). On the entropy and letter frequencies of ternary square-free words. Electronic Journal of Combinatorics, 11(1), Research Paper 14, 19 pp. (electronic).

MLA:

Richard, Christoph, and Uwe Grimm. "On the entropy and letter frequencies of ternary square-free words." Electronic Journal of Combinatorics 11.1 (2004): Research Paper 14, 19 pp. (electronic).

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