Lattice Point Inequalities for Centered Convex Bodies

Autor:	Sören Lennart Berg, Martin Henk
Rok vydání:	2016
Předmět:	Combinatorics 11H06 52C07 Planar Mathematics - Metric Geometry General Mathematics FOS: Mathematics Regular polygon Lattice (group) Centroid Metric Geometry (math.MG) Polytope Upper and lower bounds Mathematics
Zdroj:	SIAM Journal on Discrete Mathematics. 30:1148-1158
ISSN:	1095-7146 0895-4801
DOI:	10.1137/15m1031369
Popis:	We study upper bounds on the number of lattice points for convex bodies having their centroid at the origin. For the family of simplices as well as in the planar case we obtain best possible results. For arbitrary convex bodies we provide an upper bound, which extends the centrally symmetric case and which, in particular, shows that the centroid assumption is indeed much more restrictive than an assumption on the number of interior lattice points even for the class of lattice polytopes. 12 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::571f9f577519774964f4953d1bedf9e5 https://doi.org/10.1137/15m1031369 Zobrazit plný text záznamu