6 papers
The Stable Tamari Lattice
Herman Chau, Spencer Daugherty, Sean Grate +3
We introduce the stable Tamari lattice , an infinite lattice on . The -Tamari lattices on -Dyck paths of height occur as a nested family o…
Graded Betti numbers of graded Möbius algebras of uniform matroids
Louiza Fouli, Sean Grate, Selvi Kara +5
Graded Möbius algebras were a key tool in the proof of the Dowling-Wilson Top Heavy Conjecture. They are commutative algebras whose Hilbert functions recover the Whitney numbers of…
Incidence toric ideals and three-point functions
Barbara Betti, Sean Grate, Thiago Holleben +1
We study the ideal of the algebraic relations among 3-point functions from a combinatorial and topological perspective. We place this problem in the broader setting of incidence to…
Betti numbers for connected sums of graded Gorenstein artinian algebras
Nasrin Altafi, Roberta Di Gennaro, Federico Galetto +5
The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction…
The MatrixSchubert package for Macaulay2
Ayah Almousa, Sean Grate, Daoji Huang +4
We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This package has tools to construct and study matrix Schubert varieties and alternating sign matr…
Betti tables forcing failure of the Weak Lefschetz Property
Sean Grate, Hal Schenck
We study the Artinian reduction of a configuration of points , and the relation of the geometry of to Lefschetz properties of . Migliore initia…