标题： 论文 BOAT 显示英文标题

标题： Paper BOAT

摘要： 我们推导出一个公式，用于计算仿射Weyl群类型$A$中支配锥体内元素的下 Bruhat 区间的大小。 这个计数问题被简化为在某些多面体中计数格点。 我们的主要工具是将每个区间分解——或铺砌——成更小、组合上易于处理的块，我们称之为纸船。 我们还猜想该公式的推广适用于所有仿射Weyl群，限制在最低的双侧Kazhdan-Lusztig单元内，该单元包含几乎所有的元素。 显示英文摘要

摘要： 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.