Three counter-examples on semi-graphoids

Raymond Hemmecke; Jason Morton; Anne Shiu; Bernd Sturmfels; Oliver Wienand

doi:10.1017/S0963548307008838

Three counter-examples on semi-graphoids

Raymond Hemmecke
, Jason Morton
, Anne Shiu
, Bernd Sturmfels
, Oliver Wienand

Otto-von-Guericke University
University of California at Berkeley
University of Kaiserslautern

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Semi-graphoids 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 S_n. In this paper we resolve two problems on semigraphoids posed in Studeny's book (2005), and we answer a related question of Postnikov, Reiner and Williams on generalized permutohedra. We also study the semigroup and the toric ideal associated with semi-graphoids.

Original language	English
Pages (from-to)	239-257
Number of pages	19
Journal	Combinatorics Probability and Computing
Volume	17
Issue number	2
DOIs	https://doi.org/10.1017/S0963548307008838
State	Published - Mar 2008
Externally published	Yes

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Three counter-examples on semi-graphoids

Abstract

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