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math.CO2025
Absolute incidence theorems and tilings
Lukas Kühne, Matt Larson
We give a precise definition of incidence theorems in plane projective geometry and introduce the notion of ``absolute incidence theorems,'' which hold over any ring. Fomin and Pyl…
math.CO2025
Complementary vectors of simplicial complexes
Matt Larson, Alan Stapledon
We classify the complementary vectors of doubly Cohen-Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives n…
math.CO2025
Lefschetz properties of local face modules
Matt Larson, Alan Stapledon
Local face modules are modules over face rings whose Hilbert function is the local -vector of a triangulation of a simplex. We study when Lefschetz properties hold for local fac…