2023/09/25 by Youngs, Nora, Jeffs, R. Amzi, Curry, Ryan +1
paper · doi:10.20382/jocg.v14i1a7
We prove algebraic and combinatorial characterizations of the class of inductively pierced codes, resolving a conjecture of Gross, Obatake, and Youngs. Starting from an algebraic invariant of a code called its canonical form, we explain how to compute a piercing order in polynomial time, if one exists. Given a piercing order of a code, we explain how to construct a realization of the code using a well-formed collection of open balls, and classify the minimal dimension in which such a realization exists.