Recognizing and Realizing Inductively Pierced Codes
Combinatorics
2022-07-14 v1
Abstract
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.
Cite
@article{arxiv.2207.06266,
title = {Recognizing and Realizing Inductively Pierced Codes},
author = {Ryan Curry and R. Amzi Jeffs and Nora Youngs and Ziyu Zhao},
journal= {arXiv preprint arXiv:2207.06266},
year = {2022}
}
Comments
17 pages, 5 figures