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math.CO2026
Pairs of lattice complements with complementary homology
Sara Faridi, Dharm Veer, Volkmar Welker
In this paper we study whether there is a global to local principle for the homology of order complexes of finite lattices. We explore whether the non-vanishing of the homology of…
math.AC2026
Cellular resolutions of second powers of square-free monomial ideals with divisibility relations
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
Using divisibility relations between the generators of a square-free monomial ideal , we describe divisibility relations between the generators of the second power . We the…
math.AC2026
Symbolic powers and integral closures via extremal ideals
Trung Chau, Art Duval, Sara Faridi +3
This paper demonstrates that extremal ideals can be used to great effect to compute integral closures of powers and symbolic powers of square-free monomial ideals. We show that the…