Aranžmani hiperravnina

master's thesis

• Author: Damjan Murković
• Mentor: Dragutin Svrtan (mentor)
• Mentor: Goran Igaly (mentor)
• Committee member: Goran Igaly (predsjednik povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu upoznali smo se sa raznim aranžmanima hiperravnina i elementarnim pojmovima povezanim uz aranžmane hiperravnina. Istražili smo tehnike računanja područja aranžmana, kao što su brisanje-ograničavanje, korištenje karakterističnog polinoma te metoda konačnih polja. Kroz rad smo dokazali nekoliko važnijih teorema među kojim se ističe Zaslavskyjev teorem po svojoj važnosti, i iz kojega slijede mnogi rezultati. Na više primjera smo pokazali primjenu teorije i izračunali broj područja raznih aranžmana.

Abstract (english)

n this work various hyperplane arrangements have been explored and we introduced many basic terms connected with hyperplane arrangements. Technics for counting regions of arrangements were explained, such as deletion-restriction, using characteristic polynomial and finite field method. We proved several important theorems, most importantly Zaslavsky theorem, which leads to many results. On numerous examples we showed application of theory and computed the number of regions of various arrangements.

• Keywords: aranžmani hiperravnina; Zaslavskyjev teorem; računanje područja aranžmana
• Keywords (english): hyperplane arrangements; Zaslavsky theorem; counting regions of arrangements
• Language: croatian
• URN:NBN: urn:nbn:hr:217:905200
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-28 08:49:22