Barany, I;
Bureaux, J;
Lund, B;
(2018)
Convex cones, integral zonotopes, limit shape.
Advances in Mathematics
, 331
pp. 143-169.
10.1016/j.aim.2018.03.031.
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Abstract
Given a convex cone C in R d , an integral zonotope T is the sum of segments [0, vi] (i = 1, . . . , m) where each vi ∈ C is a vector with integer coordinates. The endpoint of T is k = Pm 1 vi. Let T (C, k) be the family of all integral zonotopes in C whose endpoint is k ∈ C. We prove that, for large k, the zonotopes in T (C, k) have a limit shape, meaning that, after suitable scaling, the overwhelming majority of the zonotopes in T (C, k) are very close to a fixed convex set. We also establish several combinatorial properties of a typical zonotope in T (C, k).
Type: | Article |
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Title: | Convex cones, integral zonotopes, limit shape |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1016/j.aim.2018.03.031 |
Publisher version: | http://doi.org/10.1016/j.aim.2018.03.031 |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Convex cones, Integral zonotopes, Integer partitions, Limit shape |
UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery.ucl.ac.uk/id/eprint/1522761 |
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