Minkowski summands of cubes

Federico Castillo; Joseph Doolittle; Bennet Goeckner; Michael S. Ross; Li Ying

doi:10.1112/blms.12610

Minkowski summands of cubes

Federico Castillo^*, Joseph Doolittle, Bennet Goeckner, Michael S. Ross, Li Ying

^*Corresponding author for this work

Institute of Geometry (5070)

Research output: Contribution to journal › Article › peer-review

Abstract

In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable. Nevertheless, we show that the type cone of the product of simplices is simplicial. This remarkably simple result derives from insights about rainbow point configurations and the work of McMullen.

Original language	English
Pages (from-to)	825-1166
Journal	Bulletin of the London Mathematical Society
Volume	54
Issue number	3
DOIs	https://doi.org/10.1112/blms.12610
Publication status	Published - 2022

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10.1112/blms.12610

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title = "Minkowski summands of cubes",

abstract = "In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable. Nevertheless, we show that the type cone of the product of simplices is simplicial. This remarkably simple result derives from insights about rainbow point configurations and the work of McMullen.",

author = "Federico Castillo and Joseph Doolittle and Bennet Goeckner and Ross, {Michael S.} and Li Ying",

year = "2022",

doi = "10.1112/blms.12610",

language = "English",

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journal = "Bulletin of the London Mathematical Society",

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T1 - Minkowski summands of cubes

AU - Castillo, Federico

AU - Doolittle, Joseph

AU - Goeckner, Bennet

AU - Ross, Michael S.

AU - Ying, Li

PY - 2022

Y1 - 2022

N2 - In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable. Nevertheless, we show that the type cone of the product of simplices is simplicial. This remarkably simple result derives from insights about rainbow point configurations and the work of McMullen.

AB - In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable. Nevertheless, we show that the type cone of the product of simplices is simplicial. This remarkably simple result derives from insights about rainbow point configurations and the work of McMullen.

U2 - 10.1112/blms.12610

DO - 10.1112/blms.12610

M3 - Article

SN - 0024-6093

VL - 54

SP - 825

EP - 1166

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 3

ER -

Minkowski summands of cubes

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