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On Hankel Determinantal Matroids
Abstract
We initiate a study of the algebraic matroid associated to the ideal generated by the (r+1)-minors of a Hankel matrix of variables. We prove that this matroid is uniform, that is, a coordinate projection from the corresponding Hankel determinantal variety is generically finite if and only if it preserves at least 2r anti-diagonals. For such projections, we establish bounds on the degree. These results are of significance to the problem of Hankel low-rank matrix completion.
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BibTeX
@misc{reed2026hankel,
title = {{On Hankel Determinantal Matroids}},
author = {Ethan Reed and Manolis C. Tsakiris},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27554},
eprint = {2610.27554},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27554},
}
RIS
TY - UNPB
TI - On Hankel Determinantal Matroids
AU - Ethan Reed
AU - Manolis C. Tsakiris
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27554
UR - https://arxiv.org/abs/2610.27554
AB - We initiate a study of the algebraic matroid associated to the ideal generated by the (r+1)-minors of a Hankel matrix of variables. We prove that this matroid is uniform, that is, a coordinate projection from the corresponding Hankel determinantal variety is generically finite if and only if it preserves at least 2r anti-diagonals. For such projections, we establish bounds on the degree. These results are of significance to the problem of Hankel low-rank matrix completion.
ER -