The authors define extra slow Tamari lattices on faithfully balanced tableaux, prove they are lattices that are semidistributive, trim, polygonal and congruence uniform, describe their join-irreducibles via three-color roots, and obtain enumerative results.
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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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The extra slow Tamari lattice
The authors define extra slow Tamari lattices on faithfully balanced tableaux, prove they are lattices that are semidistributive, trim, polygonal and congruence uniform, describe their join-irreducibles via three-color roots, and obtain enumerative results.
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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.