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Three Counter-Examples on Semi-Graphoids

Published online by Cambridge University Press:  01 March 2008

RAYMOND HEMMECKE ,
JASON MORTON ,
ANNE SHIU ,
BERND STURMFELS  and
OLIVER WIENAND
RAYMOND HEMMECKE
Affiliation:
Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany (e-mail: hemmecke@imo.math.uni-magdeburg.de)
JASON MORTON
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA (e-mail: mortonj@math.berkeley.edu, annejls@math.berkeley.edu, bernd@math.berkeley.edu)
ANNE SHIU
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA (e-mail: mortonj@math.berkeley.edu, annejls@math.berkeley.edu, bernd@math.berkeley.edu)
BERND STURMFELS
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA (e-mail: mortonj@math.berkeley.edu, annejls@math.berkeley.edu, bernd@math.berkeley.edu)
OLIVER WIENAND
Affiliation:
Fachbereich Mathematik, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany (e-mail: wienand@mathematik.uni-kl.de)
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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 Sn. In this paper we resolve two problems on semi-graphoids posed in Studený'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.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 2 , March 2008 , pp. 239 - 257
Copyright
Copyright © Cambridge University Press 2007

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