Helly-type theorems for abstract convexity spaces = 추상 볼록 공간에서의 헬리타입 정리들

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In the standard d-dimensional Euclidean convexity space, it is known that the colorful Helly number and the fractional Helly number are both d+1. We prove that in an abstract convexity space with bounded Radon number, the colorful Helly number and the weak fractional Helly number are bounded. To prove these results, we define convexity invariants for abstract simplicial complexes and show several correspondences between convexity invariants of convexity spaces and convexity invariants of nerve complexes. Furthermore, we show a simplification of Bukh’s counterexample for Eckhoff's conjecture as another application of these correspondences.
Advisors
Holmsen, Andreasresearcher홈슨 안드레아스researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2019
Identifier
325007
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수리과학과, 2019.2,[iii, 29 p. :]

Keywords

Abstract convexity space▼aradon's lemma▼acolorful Helly theorem▼afractional helly theorem▼aeckhoff's conjecture; 추상 볼록 공간▼a라돈의 정리▼a알록달록한 헬리 정리▼a부분적 헬리 정리▼a에크호프의 추측

URI
http://hdl.handle.net/10203/266408
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=843278&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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