Paper BOAT
Combinatorics
2025-12-11 v3 Group Theory
Representation Theory
Abstract
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 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.
Cite
@article{arxiv.2504.04489,
title = {Paper BOAT},
author = {Federico Castillo and Damian de la Fuente and Nicolas Libedinsky and David Plaza},
journal= {arXiv preprint arXiv:2504.04489},
year = {2025}
}
Comments
35 pages, 6 figures