English

An algorithm to construct the Le diagram associated to a Grassmann necklace

Combinatorics 2018-03-06 v1

Abstract

Le diagrams and Grassmann necklaces both index the collection of positroids in the nonnegative Grassmannian Gr0(k,n)Gr_{\geq 0}(k,n), but they excel at very different tasks: for example, the dimension of a positroid is easily extracted from its Le diagram, while the list of bases of a positroid is far more easily obtained from its Grassmann necklace. Explicit bijections between the two are therefore desirable. An algorithm for turning a Le diagram into a Grassmann necklace already exists; in this note we give the reverse algorithm.

Cite

@article{arxiv.1803.01726,
  title  = {An algorithm to construct the Le diagram associated to a Grassmann necklace},
  author = {Susama Agarwala and Sian Fryer},
  journal= {arXiv preprint arXiv:1803.01726},
  year   = {2018}
}

Comments

6 pages

R2 v1 2026-06-23T00:42:32.585Z