Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
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All lattice path matroids are Ehrhart positive, unifying prior results and implying positivity for Schubert matroids while supporting conjectures on positroids and Schubitopes.
The box complex realizes the canonical join complex of alt ν-Tamari lattices and is vertex decomposable, with Euler characteristic and top homology independent of δ.
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Orlik--Solomon sheaf homology of geometric lattices
Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.
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Ehrhart positivity for lattice path matroids
All lattice path matroids are Ehrhart positive, unifying prior results and implying positivity for Schubert matroids while supporting conjectures on positroids and Schubitopes.
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A combinatorial model for the canonical join complex of alt $\nu$-Tamari lattices
The box complex realizes the canonical join complex of alt ν-Tamari lattices and is vertex decomposable, with Euler characteristic and top homology independent of δ.