On the f-vectors of Gelfand-Cetlin polytopes
Combinatorics
2021-01-11 v2 Algebraic Geometry
Symplectic Geometry
Abstract
A Gelfand-Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent description of the face structure of a GC-polytope in terms of so called the face structure of a ladder diagram. Using our description, we obtain a partial differential equation whose solution is the exponential generating function of f-vectors of GC-polytopes. This solves the open problem (2) posed by Gusev, Kritchenko, and Timorin in [GKT].
Keywords
Cite
@article{arxiv.1606.05957,
title = {On the f-vectors of Gelfand-Cetlin polytopes},
author = {Byung Hee An and Yunhyung Cho and Jang Soo Kim},
journal= {arXiv preprint arXiv:1606.05957},
year = {2021}
}
Comments
14 pages