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