4 papers
Bruhat intervals that are large hypercubes
Jordan Ellenberg, Nicolas Libedinsky, David Plaza +2
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group . Using permutations suggested by AlphaEvolve (an evolutionary coding ag…
Atomic decomposition for an affine Weyl group of type
Bárbara Muniz, David Plaza, Claudia Rojas-andías
We show that the elements of the Kazhdan--Lusztig basis of the spherical Hecke algebra of type have an atomic decomposition. As a by-product, we obtain a new algorithm to com…
Paper BOAT
Federico Castillo, Damian de la Fuente, Nicolas Libedinsky +1
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 . This enumeration problem is reduced to c…
On the size of Bruhat intervals
Federico Castillo, Damian de la Fuente, Nicolas Libedinsky +1
For affine Weyl groups and elements associated to dominant coweights, we present a convex geometry formula for the size of the corresponding lower Bruhat intervals. Extensive compu…