eprintid: 1445801
rev_number: 9
eprint_status: archive
userid: 636
dir: disk0/01/44/58/01
datestamp: 2016-08-10 13:39:37
lastmod: 2016-08-10 13:39:37
status_changed: 2016-08-10 13:39:37
type: thesis
metadata_visibility: show
item_issues_count: 0
creators_name: Prodromou, M.
title: Combinatorial problems at the interface of discrete and convex geometry.
ispublished: unpub
divisions: F59
note: Thesis digitised by Proquest
abstract: This thesis consists of three chapters. The first two chapters concern lattice points and convex sets. In the first chapter we consider convex lattice polygons with minimal perimeter. Let n be a positive integer and any norm in R2. Denote by B the unit ball of and Vb,u the class of convex lattice polygons with n vertices and least -perimeter. We prove that after suitable normalisation, all members of Vb,u tend to a fixed convex body, as n > oo. In the second chapter we consider maximal convex lattice polygons inscribed in plane convex sets. Given a convex compact set K CM2 what is the largest n such that K contains a convex lattice n-gon We answer this question asymptotically. It turns out that the maximal n is related to the largest affine perimeter that a convex set contained in K can have. This, in turn, gives a new characterisation of Ko, the convex set in K having maximal affine perimeter. In the third chapter we study a combinatorial property of arbitrary finite subsets of Rd. Let X C Rd be a finite set, coloured with J colours. Then X contains a rainbow subset 7 CX, such that any ball that contains Y contains a positive fraction of the points of X.
date: 2005
id_number: PQ ETD:593125
oa_status: green
full_text_type: other
thesis_class: doctoral_open
language: eng
thesis_view: UCL_Thesis
primo: open
primo_central: open_green
verified: verified_manual
full_text_status: public
pages: 88
institution: University of London
thesis_type: Doctoral
citation:        Prodromou, M.;      (2005)    Combinatorial problems at the interface of discrete and convex geometry.                   Doctoral thesis , University of London.     Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1445801/1/U593125.pdf