Asymptotic number of isometric generalized Fibonacci cubes

Authors:
Sandi Klavar;Sergey Shpectorov
Affiliations:
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia and Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia;School of Mathematics, University of Birmingham, United Kingdom
Venue:
European Journal of Combinatorics
Year:
2012

Citing 7
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The index of a binary word

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Abstract

For a binary word f, let Q"d(f) be the subgraph of the d-dimensional cube Q"d induced on the set of all words that do not contain f as a factor. Let G"n be the set of words f of length n that are good in the sense that Q"d(f) is isometric in Q"d for all d. It is proved that lim"n"-"~|G"n|/2^n exists. Estimates show that the limit is close to 0.08, that is, about eight percent of all words are good.