English

A finite totally nonnegative Grassmannian

Combinatorics 2025-10-28 v2

Abstract

We introduce totally nonnegative Grassmannians over finite fields where an element of a finite field is nonnegative if it is a square of an element of the finite field. Explicit point counts are given in some special cases where we find new interpretations of sequences in the On-Line Encyclopedia of Integer Sequences (OEIS). We compare and contrast the theory of totally nonnegative Grassmannians over a finite field with the traditional case of the field of real numbers.

Keywords

Cite

@article{arxiv.2410.06177,
  title  = {A finite totally nonnegative Grassmannian},
  author = {John Machacek},
  journal= {arXiv preprint arXiv:2410.06177},
  year   = {2025}
}

Comments

v2 contains minor corrections

R2 v1 2026-06-28T19:13:14.146Z