A tropical isoperimetric inequality

Jules Depersin; Stéphane Gaubert; Michael Joswig

A tropical isoperimetric inequality

Jules Depersin
, Stéphane Gaubert
, Michael Joswig

TU Berlin

Research output: Contribution to conference › Paper › peer-review

Abstract

We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an interesting class of ordinary convex polytopes, characterizing the equality case in the isoperimetric inequality. This study is motivated by open complexity questions concerning linear optimization and its tropical analogs.

Original language	English
Publication status	Published - 1 Jan 2006
Event	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom Duration: 9 Jul 2017 → 13 Jul 2017

Conference

Conference	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
Country/Territory	United Kingdom
City	London
Period	9/07/17 → 13/07/17

Keywords

Idempotent measures
Log-limit sets
Polytopes
Tropical geometry
Volume

Cite this

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title = "A tropical isoperimetric inequality",

abstract = "We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an interesting class of ordinary convex polytopes, characterizing the equality case in the isoperimetric inequality. This study is motivated by open complexity questions concerning linear optimization and its tropical analogs.",

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T1 - A tropical isoperimetric inequality

AU - Depersin, Jules

AU - Gaubert, Stéphane

AU - Joswig, Michael

PY - 2006/1/1

Y1 - 2006/1/1

N2 - We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an interesting class of ordinary convex polytopes, characterizing the equality case in the isoperimetric inequality. This study is motivated by open complexity questions concerning linear optimization and its tropical analogs.

AB - We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an interesting class of ordinary convex polytopes, characterizing the equality case in the isoperimetric inequality. This study is motivated by open complexity questions concerning linear optimization and its tropical analogs.

KW - Idempotent measures

KW - Log-limit sets

KW - Polytopes

KW - Tropical geometry

KW - Volume

UR - https://www.scopus.com/pages/publications/85091912656

M3 - Paper

AN - SCOPUS:85091912656

T2 - 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017

Y2 - 9 July 2017 through 13 July 2017

ER -

A tropical isoperimetric inequality

Abstract

Conference

Keywords

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