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3 papers
Asymptotic Degree of Random Monomial Ideals
Lily Silverstein, Dane Wilburne, Jay Yang
One of the fundamental invariants connecting algebra and geometry is the degree of an ideal. In this paper we derive the probabilistic behavior of degree with respect to the versat…
Average Behavior of Minimal Free Resolutions of Monomial Ideals
Jesús A. De Loera, Serkan Hoşten, Robert Krone +1
We describe the typical homological properties of monomial ideals defined by random generating sets. We show that, under mild assumptions, random monomial ideals (RMI's) will almos…
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…