2006/10/15 by Raymond Hemmecke, Hemmecke, Raymond, Jason Morton +7 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Fuzzy and Soft Set Theory #Statistics Theory (math.ST) #math.CO #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0610451
arxiv created 2006/10/15 · openalex publication_date 2006/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.