论文标题
阳性plücker树证书的非现实性
Positive Plücker tree certificates for non-realizability
论文作者
论文摘要
我们介绍了一种新方法，以找到简单球的非可交易性证书：我们展示了经典的3-期Plücker关系的单一组合，该组合产生了在任何实现Sigma的实现中都可以肯定的决定因素的产物的总和；但是他们的总和应该消失，矛盾。使用这种技术，我们首次证明了由Novik和Zheng构建的一个高度邻居的中央对称球体构建的平衡2-邻居三杆球，以及Criado和Santos引入的几种组合型prismatots。实际上，该方法适用于可定向的伪模型，而不仅仅是球形。
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 Plücker 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 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.
