Hyperplane arrangements with a lattice of regions
Discrete & Computational Geometry
Handbook of combinatorics (vol. 2)
Kazhdan-Lusztig and R-polynomials from a combinatorial point of view
Discrete Mathematics - selected papers in honor of Adriano Garsia
More on the combinatorial invariance of Kazhdan--Lusztig polynomials
Journal of Combinatorial Theory Series A
Pattern avoidance and the Bruhat order
Journal of Combinatorial Theory Series A
Bruhat intervals as rooks on skew Ferrers boards
Journal of Combinatorial Theory Series A
The maximum number of atoms of Bruhat intervals in the symmetric groups
European Journal of Combinatorics
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We determine all isomorphism classes of intervals of length 4 in the Bruhat order on the Weyl groups A4, B4, D4 and F4. It turns out that there are 24 of them (some of which are dual to each other). Work of Dyer allows us to conclude that these are the only intervals of length 4 that can occur in the Bruhat order on any Weyl group. We also determine the intervals that arise already in the smaller classes of simply laced Weyl groups and symmetric groups.Our method combines theoretical arguments and computer calculations. We also present an independent, completely computerized, approach.