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math.CO2024
Reduced words for reflections in Weyl groups
Elizabeth Milićević
The reflections in a Coxeter group are defined as conjugates of a single generator, and thus admit palindromic expressions as products of generators. Our main result gives closed f…
math.CO2024
Crystal Chute Moves on Pipe Dreams
Sarah Gold, Elizabeth Milićević, Yuxuan Sun
Schubert polynomials represent a basis for the cohomology of the complete flag variety and thus play a central role in geometry and combinatorics. In this context, Schubert polynom…
math.CO2023
Alcove Walks and GKM Theory for Affine Flags
Elizabeth Milićević, Kaisa Taipale
We develop the GKM theory for the torus-equivariant cohomology of the affine flag variety using the combinatorics of alcove walks. Dual to the usual GKM setup, which depicts the or…