Upper Bounds on Covering Minima of Convex Bodies

Fuente: arXiv
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Autore principale: Krivokuća, Katarina
Natura: Preprint
Pubblicazione: 2026
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author Krivokuća, Katarina
author_facet Krivokuća, Katarina
contents We give two new upper bounds on the covering minima of convex bodies, depending on covering minima of certain projections and intersections with linear subspaces. We show one bound to be sharp for direct sums of two convex bodies, generalizing previous results on the covering radius and lattice width of direct sums. We apply our results to standard terminal simplices, reducing the gap between the upper and lower bounds in a conjecture of Gonzaléz Merino and Schymura (2017), which gives insight on a conjecture of Codenotti, Santos and Schymura (2021) on the maximal covering radius of a non-hollow lattice polytope.
format Preprint
id arxiv_https___arxiv_org_abs_2601_15173
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Upper Bounds on Covering Minima of Convex Bodies
Krivokuća, Katarina
Combinatorics
Metric Geometry
52B11, 52C07, 52B12, 52B20, 52B55
We give two new upper bounds on the covering minima of convex bodies, depending on covering minima of certain projections and intersections with linear subspaces. We show one bound to be sharp for direct sums of two convex bodies, generalizing previous results on the covering radius and lattice width of direct sums. We apply our results to standard terminal simplices, reducing the gap between the upper and lower bounds in a conjecture of Gonzaléz Merino and Schymura (2017), which gives insight on a conjecture of Codenotti, Santos and Schymura (2021) on the maximal covering radius of a non-hollow lattice polytope.
title Upper Bounds on Covering Minima of Convex Bodies
topic Combinatorics
Metric Geometry
52B11, 52C07, 52B12, 52B20, 52B55
url https://arxiv.org/abs/2601.15173