Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Conference papers

Triangulations of root polytopes and reduced forms (Extended abstract)

Abstract : The type $A_n$ root polytope $\mathcal{P}(A_n^+)$ is the convex hull in $\mathbb{R}^{n+1}$ of the origin and the points $e_i-e_j$ for $1 \leq i < j \leq n+1$. Given a tree $T$ on vertex set $[n+1]$, the associated root polytope $\mathcal{P}(T)$ is the intersection of $\mathcal{P}(A_n^+)$ with the cone generated by the vectors $e_i-e_j$, where $(i, j) \in E(T)$, $i < j$. The reduced forms of a certain monomial $m[T]$ in commuting variables $x_{ij}$ under the reduction $x_{ij} x_{jk} \to x_{ik} x_{ij} + x_{jk} x_{ik} + \beta x_{ik}$, can be interpreted as triangulations of $\mathcal{P}(T)$. 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 $\mathcal{P}(T)$ in which each simplex corresponds to a noncrossing alternating forest.
Complete list of metadata

Cited literature [4 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Thursday, August 20, 2015 - 11:06:21 AM
Last modification on : Wednesday, June 26, 2019 - 2:48:03 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:19:34 AM


Publisher files allowed on an open archive




Karola Mészáros. Triangulations of root polytopes and reduced forms (Extended abstract). 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.647-660, ⟨10.46298/dmtcs.2681⟩. ⟨hal-01185373⟩



Record views


Files downloads