ASYMPTOTIC DEGREE OF RANDOM MONOMIAL IDEALS

One of the fundamental invariants connecting algebra and geometry is degree an ideal. In this paper we derive probabilistic behavior with respect to versatile Erdős–Rényi-type model for random monomial ideals. We study staircase structure associated a ideal, show that in case shape diagram approximately hyperbolic, robust across several models. Since discrete volume under related summatory higher-order divisor function studied number theory, use connection our control over asymptotic Another way compute ideal standard pair decomposition. This derives bounds on pairs indexed by any subset ring variables. The maximal subsets give count degree, as well being more nuanced invariant