5 papers
Antichain Simplices
Benjamin Braun, Brian Davis
To each lattice simplex we associate a poset encoding the additive structure of lattice points in the fundamental parallelepiped for . When this poset is an antichain, we sa…
Predicting the Integer Decomposition Property via Machine Learning
Brian Davis
In this paper we investigate the ability of a neural network to approximate algebraic properties associated to lattice simplices. In particular we attempt to predict the distributi…
Complete intersection P-partition rings
Brian Davis
We present an alternate proof of a result of Féray and Reiner characterizing posets whose -partition rings are complete intersections. This shortened proof relates the complete…
Rationality of Poincaré Series for a Family of Lattice Simplices
Benjamin Braun, Brian Davis
We investigate multi-graded Gorenstein semigroup algebras associated with an infinite family of reflexive lattice simplices. For each of these algebras, we prove that their multigr…
Unlabeled Signed Graph Coloring
Brian Davis
We extend the work of Hanlon on the chromatic polynomial of an unlabeled graph to define the unlabeled chromatic polynomial of an unlabeled signed graph. Explicit formulas are pres…