17 citations · 48 across the 14 of their papers we have counts for
7 papers · 1 filter
Predicting the cardinality and maximum degree of a reduced Gröbner basis
Shahrzad Jamshidi, Eric Kang, Sonja Petrović
We construct neural network regression models to predict key metrics of complexity for Gröbner bases of binomial ideals. This work illustrates why predictions with neural networks…
Hypergraph encodings of arbitrary toric ideals
Sonja Petrović, Apostolos Thoma, Marius Vladoiu
Relying on the combinatorial classification of toric ideals using their bouquet structure, we focus on toric ideals of hypergraphs and study how they relate to general toric ideals…
Random Monomial Ideals
Jesus A. De Loera, Sonja Petrovic, Lily Silverstein +2
Inspired by the study of random graphs and simplicial complexes, and motivated by the need to understand average behavior of ideals, we propose and study probabilistic models of ra…
Combinatorial degree bound for toric ideals of hypergraphs
Elizabeth Gross, Sonja Petrović
Associated to any hypergraph is a toric ideal encoding the algebraic relations among its edges. We study these ideals and the combinatorics of their minimal generators, and derive…
Toric algebra of hypergraphs
Sonja Petrović, Despina Stasi
The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their genera…
Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees
Sonja Petrović, Erik Stokes
There are two seemingly unrelated ideals associated with a simplicial complex Δ. One is the Stanley-Reisner ideal I_Δ, the monomial ideal generated by minimal non-faces of Δ, well-…
Toric ideals of phylogenetic invariants for the general group-based model on claw trees
Julia Chifman, Sonja Petrović
We address the problem of studying the toric ideals of phylogenetic invariants for a general group-based model on an arbitrary claw tree. We focus on the group and ch…