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math.CO2026
Affine Higher Bruhat Orders
Sara Billey, Herman Chau, Kevin Liu
The higher Bruhat orders are partial orders originally constructed by Manin and Schechtman, with an equivalent construction from Ziegler. These partial orders generalize the weak o…
math.CO2026
A ChatGPT-assisted Triangle Characterization of Affine Permutation Inversion Graphs
Sara C. Billey, Herman Chau, Kevin Liu
Inversion sets of permutations in the affine symmetric group were studied extensively by Björner and Brenti. One of their methods for encoding an inversion set is…
math.CO2026
Commutation classes of reduced words and higher Bruhat orders for affine permutations
Sara Billey, Herman Chau, Kevin Liu
The higher Bruhat orders are partial orders that generalize the weak order on the symmetric group , and the second higher Bruhat order is a poset on commutation classes of red…