Three Counterexamples on Semigraphoids
Combinatorics
2007-06-13 v1 Statistics Theory
Statistics Theory
Abstract
Semigraphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection arrangement of the symmetric group. We resolve two problems on semigraphoids posed in Studeny's book, and we answer a related question by Postnikov, Reiner, and Williams on generalized permutohedra. We also study the semigroup and the toric ideal associated with semigraphoids.
Cite
@article{arxiv.math/0610451,
title = {Three Counterexamples on Semigraphoids},
author = {Raymond Hemmecke and Jason Morton and Anne Shiu and Bernd Sturmfels and Oliver Wienand},
journal= {arXiv preprint arXiv:math/0610451},
year = {2007}
}