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

Mathematics

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

15 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 (US)
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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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Three counter-examples on semi-graphoids

Abstract

All Science Journal Classification (ASJC) codes

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