Combinatorial formulas for -coordinates in a totally nonnegative Grassmannian

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Talaska, Kelli

关键词: Positroid;    Totally nonnegative Grassmannian;    Le-diagram;   

DOI  :  10.1016/j.jcta.2009.10.006

来源: Elsevier

【 摘 要 】

Postnikov constructed a decomposition of a totally nonnegative Grassmannian (Gr(kn))>= 0 Into positroid cells We provide combinatorial formulas that allow one to decide which cell a given point in (Gr(kn))>= 0 belongs to and to determine affine coordinates of the point within this cell This simplifies Postnikov s description of the inverse boundary measurement map and generalizes formulas for the top cell given by Speyer and Williams In addition we identify a particular subset of Plucker coordinates as a totally positive base for the set of non-vanishing Plucker coordinates for a given positroid cell (C) 2009 Elsevier Inc All rights reserved

【 授权许可】

Free