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arXiv · 1201.0529

Some acyclic systems of permutations are not realizable by triangulations of a product of simplices

Francisco Santos
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Abstract

The acyclic system conjecture of Ardila and Ceballos can be interpreted as saying the following: "Every triangulation of the 3-skeleton of a product of two simplices can be extended to a triangulation of the whole product". We show a counter-example to this. Motivation for this conjecture comes from a related conjecture, the "spread-out simplices" conjecture of Ardila and Billey. We give some necessary conditions that counter-examples to this second conjecture (if they exist) must satisfy.

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Francisco Santos. 2012-01-05. Some acyclic systems of permutations are not realizable by triangulations of a product of simplices. https://arxiv.org/abs/1201.0529

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