Noncrossing sets and a Graßmann associahedron

1Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

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 ([nk]) induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset given by the product [k] × [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 Gk,n~= Gn-k,n. This simplicial complex is closely related to the weak separability complex introduced by Zelevinsky and Leclerc.

References Powered by Scopus

Two poset polytopes

315Citations
N/AReaders
Get full text

Grassmannians and cluster algebras

210Citations
N/AReaders
Get full text

Alcoved polytopes, I

79Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Geometry of ν-tamari lattices in types A and B

25Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Santos, F., Stump, C., & Welker, V. (2014). Noncrossing sets and a Graßmann associahedron. In Discrete Mathematics and Theoretical Computer Science (pp. 609–620). Discrete Mathematics and Theoretical Computer Science. https://doi.org/10.46298/dmtcs.2427

Readers' Seniority

Tooltip

PhD / Post grad / Masters / Doc 4

100%

Readers' Discipline

Tooltip

Mathematics 4

100%

Save time finding and organizing research with Mendeley

Sign up for free