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math.CO2024
Braid graphs in simply-laced triangle-free Coxeter systems are median
Jillian Barnes, Jadyn V. Breland, Dana C. Ernst +1
Any two reduced expressions for the same Coxeter group element are related by a sequence of commutation and braid moves. Two reduced expressions are said to be braid equivalent if…
math.CO2021
Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes
Fadi Awik, Jadyn Breland, Quentin Cadman +1
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 l…