Growth of positive words and lower bounds of the growth rate for Thompson’s groups F(p)
| Autor: | José Burillo, Victor Guba |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Monoid
Group (mathematics) Computer Science::Information Retrieval General Mathematics 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 01 natural sciences Upper and lower bounds Combinatorics New normal 0103 physical sciences Computer Science::General Literature 010307 mathematical physics Growth rate 0101 mathematics Mathematics |
| Zdroj: | International Journal of Algebra and Computation. 27:1-21 |
| ISSN: | 1793-6500 0218-1967 |
| Popis: | Let [Formula: see text], [Formula: see text] be the family of generalized Thompson’s groups. Here, [Formula: see text] is the famous Richard Thompson’s group usually denoted by [Formula: see text]. We find the growth rate of the monoid of positive words in [Formula: see text] and show that it does not exceed [Formula: see text]. Also, we describe new normal forms for elements of [Formula: see text] and, using these forms, we find a lower bound for the growth rate of [Formula: see text] in its natural generators. This lower bound asymptotically equals [Formula: see text] for large values of [Formula: see text]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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