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master's thesis
Vjerojatnosna metoda u ekstremalnim kombinatornim problemima
2018. urn:nbn:hr:166:207423
Zec, Ivana
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Zec, I. (2018). Vjerojatnosna metoda u ekstremalnim kombinatornim problemima (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:207423

Zec, Ivana. "Vjerojatnosna metoda u ekstremalnim kombinatornim problemima." Master's thesis, University of Split, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:166:207423

Zec, Ivana. "Vjerojatnosna metoda u ekstremalnim kombinatornim problemima." Master's thesis, University of Split, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:166:207423

Zec, I. (2018). 'Vjerojatnosna metoda u ekstremalnim kombinatornim problemima', Master's thesis, University of Split, Faculty of Science, accessed 19 April 2024, https://urn.nsk.hr/urn:nbn:hr:166:207423

Zec I. Vjerojatnosna metoda u ekstremalnim kombinatornim problemima [Master's thesis]. Split: University of Split, Faculty of Science; 2018 [cited 2024 April 19] Available at: https://urn.nsk.hr/urn:nbn:hr:166:207423

I. Zec, "Vjerojatnosna metoda u ekstremalnim kombinatornim problemima", Master's thesis, University of Split, Faculty of Science, Split, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:166:207423

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Metadata
TitleVjerojatnosna metoda u ekstremalnim kombinatornim problemima
Title (english)Probabilistic method in extremal combinatorics problems
AuthorIvana Zec
MentorDamir Vukičević (mentor)
Committee memberDamir Vukičević (predsjednik povjerenstva)
Committee memberAnka Golemac (član povjerenstva)
Committee memberTanja Vojković (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2018-07-12, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Vjerojatnosna metoda je snažan alat u kombinatorici i teoriji grafova. Osnovni princip vjerojatnosne metode je sljedeći. Želimo pokazati da postoji neki kombinatorni objekt koji zadovoljava neko svojstvo P. Da bismo to pokazali, promatramo proizvoljni objekt iz dobro odabranog vjerojatnosnog prostora i računamo vjerojatnost da taj objekt zadovoljava svojstvo P. Ako dobijemo da je ova vjerojatnost veća od nula, zaključujemo da objekt s traženim svojstvom P postoji. Ako ne postoji objekt koji zadovoljava svojstvo P, onda će vjerojatnost koju smo izračunali biti nula. U ovom radu pokazali smo kako primjenom vjerojatnosne metode možemo riješiti neke od problema ekstremalne kombinatorike.
Abstract (english)
The probabilistic method is a powerful tool in Combinatorics and Graph Theory. The general principle of the probabilistic method is the following. We want to show the existence of a combinatorial object satisfying a given property P. To do this, we consider a random object in a well chosen probability space and we compute the probability that such an object satisfies the property P. If we show that this probability is greater then 0, then we deduce that an object with property P exists. Indeed, if no object were satisfying property P, then the probability would be zero. In this work, we showed how to solve some of the extremal combinatorics problems by applying the probabilistic method.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:207423
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching
Course: major in computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2019-02-04 15:53:59