Asymptotic number of isometric generalized Fibonacci cubes |
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| Authors: | Sandi Klav?ar Sergey Shpectorov |
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| Affiliation: | a Faculty of Mathematics and Physics, University of Ljubljana, Sloveniab Faculty of Natural Sciences and Mathematics, University of Maribor, Sloveniac School of Mathematics, University of Birmingham, United Kingdom |
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| Abstract: | For a binary word f, let Qd(f) be the subgraph of the d-dimensional cube Qd induced on the set of all words that do not contain f as a factor. Let Gn be the set of words f of length n that are good in the sense that Qd(f) is isometric in Qd for all d. It is proved that limn→∞|Gn|/2n exists. Estimates show that the limit is close to 0.08, that is, about eight percent of all words are good. |
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