Ramseyjeva teorija na cijelim brojevima

master's thesis

• Title (english): Ramsey theory on integers
• Author: Ana Flanjak
• Mentor: Sonja Žunar (mentor)
• Committee member: Sonja Žunar (predsjednik povjerenstva)
• Committee member: Vjekoslav Kovač (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-05-05, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu razmotrili smo osnovne teoreme Ramseyjeve teorije te se također usredotočili na ranu fazu njezina razvoja. Pokazali smo kako je računanje Ramseyjevih brojeva vrlo zahtjevan proces, pri čemu je do danas poznato samo 9 netrivijalnih Ramseyjevih brojeva. Nadalje, ukazali smo na primjene Ramseyjeve teorije u rješavanju problema iz stvarnog života. Konačno, predstavili smo jedan od mogućih algoritama za računanje Ramseyjevih brojeva.

Abstract (english)

In this master’s thesis, we considered the basic theorems of Ramsey theory and focused on the early stage of its development. We have shown that the computation of Ramsey numbers is a very demanding process, as only 9 non-trivial Ramsey numbers are known to date. In addition, we highlighted the applications of Ramsey theory in solving real-life problems. Finally, we presented one of the possible algorithms for computing Ramsey numbers.

• Keywords: Ramseyjevi brojevi; problemi iz stvarnog života; algoritam za računanje Ramseyjevih brojeva
• Language: croatian
• URN:NBN: urn:nbn:hr:217:038787
• Study programme: Title: Financial and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-08 15:33:01