Theorems of carathéodory, helly, and tverberg without dimension

Karim Adiprasito; Imre Bárány; Nabil H. Mustafa

doi:https://doi.org/10.1137/1.9781611975482.143

Theorems of carathéodory, helly, and tverberg without dimension

Karim Adiprasito, Imre Bárány, Nabil H. Mustafa

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

Motivated by Barman [6], we initiate a systematic study of the ‘no-dimensional’ analogues of some basic theorems in combinatorial and convex geometry, including the colorful Carathéodory’s theorem, Tverberg’s theorem, Helly’s theorem as well as their fractional and colorful extensions.

Original language	English
Pages	2350-2360
Number of pages	11
DOIs	https://doi.org/10.1137/1.9781611975482.143
State	Published - 2019
Event	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States Duration: 6 Jan 2019 → 9 Jan 2019

Conference

Conference	30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
Country/Territory	United States
City	San Diego
Period	6/01/19 → 9/01/19

All Science Journal Classification (ASJC) codes

Software
General Mathematics

Access to Document

https://doi.org/10.1137/1.9781611975482.143

Cite this

@conference{64b30313bed74860909e82899dca3190,

title = "Theorems of carath{\'e}odory, helly, and tverberg without dimension",

abstract = "Motivated by Barman [6], we initiate a systematic study of the {\textquoteleft}no-dimensional{\textquoteright} analogues of some basic theorems in combinatorial and convex geometry, including the colorful Carath{\'e}odory{\textquoteright}s theorem, Tverberg{\textquoteright}s theorem, Helly{\textquoteright}s theorem as well as their fractional and colorful extensions.",

author = "Karim Adiprasito and Imre B{\'a}r{\'a}ny and Mustafa, {Nabil H.}",

note = "Publisher Copyright: Copyright {\textcopyright} 2019 Copyright for this paper is retained by authors.; 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 ; Conference date: 06-01-2019 Through 09-01-2019",

year = "2019",

doi = "https://doi.org/10.1137/1.9781611975482.143",

language = "الإنجليزيّة",

pages = "2350--2360",

}

TY - CONF

T1 - Theorems of carathéodory, helly, and tverberg without dimension

AU - Adiprasito, Karim

AU - Bárány, Imre

AU - Mustafa, Nabil H.

PY - 2019

Y1 - 2019

N2 - Motivated by Barman [6], we initiate a systematic study of the ‘no-dimensional’ analogues of some basic theorems in combinatorial and convex geometry, including the colorful Carathéodory’s theorem, Tverberg’s theorem, Helly’s theorem as well as their fractional and colorful extensions.

AB - Motivated by Barman [6], we initiate a systematic study of the ‘no-dimensional’ analogues of some basic theorems in combinatorial and convex geometry, including the colorful Carathéodory’s theorem, Tverberg’s theorem, Helly’s theorem as well as their fractional and colorful extensions.

UR - http://www.scopus.com/inward/record.url?scp=85066949545&partnerID=8YFLogxK

U2 - https://doi.org/10.1137/1.9781611975482.143

DO - https://doi.org/10.1137/1.9781611975482.143

M3 - محاضرة

SP - 2350

EP - 2360

T2 - 30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019

Y2 - 6 January 2019 through 9 January 2019

ER -

Theorems of carathéodory, helly, and tverberg without dimension

Abstract

Conference

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this