On powers of Plücker coordinates and representability of arithmetic matroids

@article{Lenz2020OnPO,
  title={On powers of Pl{\"u}cker coordinates and representability of arithmetic matroids},
  author={Matthias Lenz},
  journal={Adv. Appl. Math.},
  year={2020},
  volume={112}
}
  • Matthias Lenz
  • Published 2020
  • Mathematics, Computer Science
  • Adv. Appl. Math.
  • The first problem we investigate is the following: given $k\in \mathbb{R}_{\ge 0}$ and a vector $v$ of Plucker coordinates of a point in the real Grassmannian, is the vector obtained by taking the $k$th power of each entry of $v$ again a vector of Plucker coordinates? For $k\neq 1$, this is true if and only if the corresponding matroid is regular. Similar results hold over other fields. We also describe the subvariety of the Grassmannian that consists of all the points that define a regular… CONTINUE READING

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