3 papers
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.RT2023
Brauer pairs for splendid Rickard equivalences
Jadyn V. Breland, Sam K. Miller
We define the notion of a Brauer pair of a chain complex, extending the notion of a Brauer pair of a -permutation module introduced by Boltje and Perepelitsky. In fact, the Brau…
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…