Root polytopes, triangulations, and the subdivision algebra, I

Details Root polytopes, triangulations, and the subdivision algebra, I Root polytopes, triangulations, and the subdivision algebra, I

2009-04-14

arxiv.org/abs/0904.2194v3

Mathematics

Combinatorics

27 pages, 4 figures; Added section 10 to the paper where the connection to noncommutative Groebner bases is made explicit

Scientific paper

The type A_n full root polytope is the convex hull in R^{n+1} of the origin and the points e_i-e_j for 1<= i x_{ik}x_{ij}+x_{jk}x_{ik}+\beta x_{ik}, can be interpreted as triangulations of P(T). Using these triangulations, the volume and Ehrhart polynomial of P(T) are obtained. If we allow variables x_{ij} and x_{kl} to commute only when i, j, k, l are distinct, then the reduced form of m[T] is unique and yields a canonical triangulation of P(T) in which each simplex corresponds to a noncrossing alternating forest. Most generally, the reduced forms of all monomials in the noncommutative case are unique.

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