Minkowski Summands of Cubes

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

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 › Conference 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
Article number	59
Number of pages	12
Journal	Séminaire Lotharingien de Combinatoire
Volume	85B
Publication status	Published - 2021
Event	33rd Conference on Formal Power Series and Algebraic Combinatorics: FPSAC 2021 - Virtuell, Israel Duration: 17 Jan 2022 → 20 Jan 2022

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https://www.mat.univie.ac.at/~slc/wpapers/FPSAC2021/59Castillo.pdf

Cite this

@article{cfcf6624cb9243498920bb553b4173a0,

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 = "2021",

language = "English",

volume = "85B",

journal = "S{\'e}minaire Lotharingien de Combinatoire",

issn = "1286-4889",

publisher = "Faculty of Mathematics, University of Vienna",

note = "33rd Conference on Formal Power Series and Algebraic Combinatorics : FPSAC 2021, FPSAC 2021 ; Conference date: 17-01-2022 Through 20-01-2022",

}

TY - JOUR

T1 - Minkowski Summands of Cubes

AU - Castillo, Federico

AU - Doolittle, Joseph

AU - Goeckner, Bennet

AU - Ross, Michael S.

AU - Ying, Li

PY - 2021

Y1 - 2021

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.

M3 - Conference article

VL - 85B

JO - Séminaire Lotharingien de Combinatoire

JF - Séminaire Lotharingien de Combinatoire

SN - 1286-4889

M1 - 59

T2 - 33rd Conference on Formal Power Series and Algebraic Combinatorics

Y2 - 17 January 2022 through 20 January 2022

ER -

Minkowski Summands of Cubes

Abstract

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