2025/04/06 by Castillo, Federico, de la Fuente, Damian, Libedinsky, Nicolas +1
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2504.04489
We derive a formula for computing the size of lower Bruhat intervals for elements in the dominant cone of an affine Weyl group of type A. This enumeration problem is reduced to counting lattice points in certain polyhedra. Our main tool is a decomposition -- or tiling -- of each interval into smaller, combinatorially tractable pieces, which we call paper boats. We also conjecture a generalization of this formula to all affine Weyl groups, restricted to elements in the lowest two-sided Kazhdan-Lusztig cell, which contains almost all of the elements.