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Federico Castillo
,
Damian de la Fuente
,
Nicolás Libedinsky
,
David Plaza
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2504.04489
· OA: W4416116998
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2504.04489
· OA: W4416116998
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.
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