Vjerojatnosna metoda u kombinatorici

master's thesis

• Title (english): Probabilistic method in combinatorics
• Author: Mateja Lukić
• Mentor: Vedran Krčadinac (mentor)
• Committee member: Vedran Krčadinac (predsjednik povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-07-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad obrađuje osnovne ideje i primjere vjerojatnosne metode u kombinatorici. Na početku rada se podsjećamo defnicija i rezultata iz teorije vjerojatnosti potrebnih za razumijevanje vjerojatnosne metode. Zatim obrađujemo primjere iz različitih područja kombinatorike u kojima se vidi koliko je, iako ponekad nije nužna, vjerojatnosna metoda praktična. U četvrtom poglavlju obrađujemo dodatne primjere uz pomoć indikatorskih slučajnih varijabli i svojstva linearnosti očekivanja. Također spominjemo i metodu preinaka kojom eliminiramo nedostatke nasumičnih struktura. U zadnjem dijelu rada spominjemo nekoliko primjera korištenja vjerojatnosne metode uz pomoć drugog momenta.

Abstract (english)

This thesis deals with basic ideas and examples of the probabilistic method in combinatorics. First, we recall the defnitions and results from probability theory that are necessary for understanding the probabilistic method. We, then, deal with examples from different areas of combinatorics showing how, even if it's not always necessary, probabilistic method can be practical. In the fourth chapter, we deal with additional examples using indicator random variables and linearity property of expectation. We also mention the alteration method by which we remove blemishes of random structures. In the last part of the thesis, we mention a few examples of using probabilistic method with the help of second moment.

• Keywords: indikatorske slučajne varijable; svojstvo linearnosti očekivanja; metoda preinaka
• Keywords (english): indicator random variables; linearity property of expectation; alteration method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:757853
• 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: 2021-09-15 11:39:58