Properties of tiny braids and the associated commuting graph
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In this text, we focus on a subset (called the set of tiny braids) of factors of the Garside braid and generalize some known results related to tiny braids. These generalized results, along with some combinatorics, strengthen the existing relationship between this subset and Fibonacci numbers. We also associate a commuting graph with the subset and explore its fundamental identities, including its order, diameter, girth and degree-related properties.
KeywordsFibonacci numbers Centralizer Commuting graph Positive braid Tiny braid
Mathematics Subject Classification11B39 05A15 05A05
- 4.Ashraf, R., Berceanu, B.: Simple braids, arXiv:1003.6014v1 [math.GT] (2010)