On root posets for noncrystallographic root systems

2012/12/12 by Cuntz, Michael, Stump, Christian
#20F55 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.2876

Abstract

We discuss properties of root posets for finite crystallographic root systems, and show that these properties uniquely determine root posets for the noncrystallographic dihedral types and type H₃, while proving that there does not exist a poset satisfying all of the properties in type H₄. We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type H₃ as restricted roots of type D₆, and conjecture a Hilbert polynomial for the q,t-Catalan numbers for type H₄.

Related

• Dominant regions in noncrystallographic hyperplane arrangements
• Triangulations of root polytopes
• Stability of stretched root systems, root posets, and shards
• Decorated Geometric Crystals and Polyhedral Realizations of type D_n
• Polytopal realizations of non-crystallographic associahedra