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 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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics