Journal
EXPERIMENTAL MATHEMATICS
Volume -, Issue -, Pages -Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/10586458.2021.1994487
Keywords
final polynomial; realizability; integer programming; simplicial sphere; Plucker relations
Categories
Funding
- Spanish Ministry of Education (MEC) [PID2019-106188GB-I00]
Ask authors/readers for more resources
This article presents a new method for finding a non-realizability certificate of a simplicial sphere. It can be applied not only to balanced 2-neighborly 3-spheres, but also to orientable pseudo-manifolds.
We introduce a new method for finding a non-realizability certificate of a simplicial sphere sigma: we exhibit a monomial combination of classical 3-term Plucker relations that yields a sum of products of determinants that are known to be positive in any realization of sigma; but their sum should vanish, contradiction. Using this technique, we prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere constructed by Zheng, a family of highly neighborly centrally symmetric spheres constructed by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos. The method in fact works for orientable pseudo-manifolds, not just for spheres.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available