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arXiv · 2104.12318

Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes

Fadi Awik·Jadyn Breland·Quentin Cadman·Dana C. Ernst
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Abstract

In this paper, we study the structure of braid graphs in simply-laced Coxeter systems. We prove that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a decomposition of the braid graph into a box product of the braid graphs for each link factor. When the Coxeter graph has no three-cycles, we use the decomposition to prove that braid graphs are partial cubes, i.e., can be isometrically embedded into a hypercube. For a special class of links, called Fibonacci links, we prove that the corresponding braid graphs are Fibonacci cubes.

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Fadi Awik, Jadyn Breland, Quentin Cadman, Dana C. Ernst. 2021-04-26. Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes. https://doi.org/10.1016/j.ejc.2024.103931

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