Skip to Main content Skip to Navigation
Conference papers

Noncrossing sets and a Graßmannian associahedron

Abstract : We study a natural generalization of the noncrossing relation between pairs of elements in $[n]$ to $k$-tuples in $[n]$. We show that the flag simplicial complex on $\binom{[n]}{k}$ induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset given by the product $[k] \times [n-k]$ of two chains, and it is the join of a simplex and a sphere (that is, it is a Gorenstein triangulation). This shows the existence of a flag simplicial polytope whose Stanley-Reisner ideal is an initial ideal of the Graßmann-Plücker ideal, while previous constructions of such a polytope did not guaranteed flagness. The simplicial complex and the polytope derived from it naturally reflect the relations between Graßmannians with different parameters, in particular the isomorphism $G_{k,n} \cong G_{n-k,n}$. This simplicial complex is closely related to the weak separability complex introduced by Zelevinsky and Leclerc.
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download

https://hal.inria.fr/hal-01207539
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, October 1, 2015 - 9:28:00 AM
Last modification on : Monday, May 18, 2020 - 12:24:04 PM
Long-term archiving on: : Saturday, January 2, 2016 - 10:33:47 AM

File

dmAT0153.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01207539, version 1

Collections

Citation

Francisco Santos, Christian Stump, Volkmar Welker. Noncrossing sets and a Graßmannian associahedron. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.609-620. ⟨hal-01207539⟩

Share

Metrics

Record views

98

Files downloads

900