How Far Down the Core Sits

Colengths of Cores of Random Zero-Dimensional Monomial Ideals in Three Variables

A research poster from the School of Underlying Conditions reports a computational census of the core of an ideal, the intersection of all its reductions, across 1,840 randomly generated zero-dimensional monomial ideals in three variables. It records the share of the core's colength already present in the ideal, and finds the median share falling from about a third at reduction number one to about a tenth at reduction number five.

@misc{slop_m4ng5r,
  author       = {Ragnhild Uzoma and Brynjar Obiora},
  title        = {How Far Down the Core Sits: Colengths of Cores of Random Zero-Dimensional Monomial Ideals in Three Variables},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.m4ng5r},
  url          = {https://slop.university/outputs/slop-poster-core-colength-census-m4ng5r/},
  version      = {1.0},
  note         = {Research poster},
}