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master's thesis
Catalanovi brojevi
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:965809
Babić, Jelena
University of Zagreb
Faculty of Science
Department of Mathematics

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Babić, J. (2016). Catalanovi brojevi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:965809

Babić, Jelena. "Catalanovi brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:965809

Babić, Jelena. "Catalanovi brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:965809

Babić, J. (2016). 'Catalanovi brojevi', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 April 2024, https://urn.nsk.hr/urn:nbn:hr:217:965809

Babić J. Catalanovi brojevi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 April 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:965809

J. Babić, "Catalanovi brojevi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:965809

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Metadata
TitleCatalanovi brojevi
AuthorJelena Babić
MentorDragutin Svrtan (mentor)
Committee memberDragutin Svrtan (predsjednik povjerenstva)
Committee memberLuka Grubišić (član povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-02-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Catalanovi brojevi javljaju se u mnogo kombinatornih problema, kao što su putevi u cjelobrojnoj mreži, problem zagrađivanja, problem binarnih stabala, Dyckovi putovi, triangulacije konveksnog n-terokuta, te Bertradov problem glasovanja. U ovom diplomskom radu opisani su navedeni kombinatorni problemi te pokazane bijekcije sa drugim kombinatornim objektima. Opisana su i svojstva Catalanovih brojeva. Na kraju diplomskog rada navedeni su primjeri nekih kombinatornih interpretacija koje nisu toliko poznate, te je pokazano kako se Catalanovi brojevi pojavljuju na mnogo neočekivanih mjesta.
Abstract (english)
Catalan numbers appear in many combinatorial problems, such as monotonic lattice paths along the edges of a grid with n x n square cells which do not pass above the diagonal, matching n pairs of brackets, the problem of binary trees, Dyck paths, triangulation of a convex polygon with n sides, and Bertrands ballot problem. In this study we described each of these combinatorial problems and showed bijection with other combinatorial objects. We also have described the properties of the Catalan numbers. We have concluded the work with some examples of combinatorial interpretations that are not so well known, and showed some of them how Catalan numbers appear in many unexpected places.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:965809
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of the Faculty of Science
Created on2017-01-25 14:00:32

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