Fibonacci numbers and positive braids
Rehana Ashraf, Barbu Berceanu, Ayesha Riasat
TL;DR
This paper explores the combinatorial properties of positive braids and their relation to Fibonacci numbers, analyzing their structure and enumeration within the braid group.
Contribution
It introduces new enumerative results linking Fibonacci sequences with classes of positive braids and examines the structure of the simple subgraph in the braid group's Cayley graph.
Findings
Enumerated positive, square-free, and simple braids with Fibonacci connections
Analyzed the structure of the simple subgraph of the braid group's Cayley graph
Established combinatorial links between Fibonacci numbers and braid classes
Abstract
The paper contains enumerative combinatorics for positive braids, square free braids, and simple braids, emphasizing connections with classical Fibonacci sequence. The simple subgraph of the Cayley graph of the braid group is analyzed in the final part.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Finite Group Theory Research