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master's thesis
Catalanovi brojevi
2022. urn:nbn:hr:166:382437
Tomašević, Magdalena
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Tomašević, M. (2022). Catalanovi brojevi (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:382437

Tomašević, Magdalena. "Catalanovi brojevi." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:382437

Tomašević, Magdalena. "Catalanovi brojevi." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:382437

Tomašević, M. (2022). 'Catalanovi brojevi', Master's thesis, University of Split, Faculty of Science, accessed 15 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:382437

Tomašević M. Catalanovi brojevi [Master's thesis]. Split: University of Split, Faculty of Science; 2022 [cited 2024 November 15] Available at: https://urn.nsk.hr/urn:nbn:hr:166:382437

M. Tomašević, "Catalanovi brojevi", Master's thesis, University of Split, Faculty of Science, Split, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:166:382437

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Metadata
TitleCatalanovi brojevi
Title (english)Catalan numbers
AuthorMagdalena Tomašević
MentorSnježana Braić (mentor)
Committee memberSnježana Braić (predsjednik povjerenstva)
Committee memberŽeljka Zorić (član povjerenstva)
Committee memberStipe Marić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2022-07-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Catalanovi brojevi javljaju se pri prebrojavanju iznenađujuće mnogo kombinatornih i drugih matematičkih objekata. U ovom radu detaljnije su opisani problem triangulacije konveksnog n-terokuta, problem zagrada, problem binarnih stabala, problem putova u cjelobrojnoj mreži, problem Dyckovih planinskih putova te Bertrandov problem glasovanja. Naposlijetku je pokazano da rješenja tih problema odgovaraju n-tom Catalanovom broju. Radi lakšeg manipuliranja nizom brojeva, izvedena je i odgovarajuća funkcija izvodnica te je tako dobivena formula za računanje općeg člana niza. Konačno, navedene su još neke zanimljive interpretacije Catalanovih brojeva.
Abstract (english)
Catalan’s numbers appear in various combinatorical and other mathematical objects. In this paper convex polygon triangulation as well as balanced parentheses, problem of binary trees, problem of lattice paths, problem of Dyck paths and Bertrand’s ballot problem are being analysed. Ultimately, it was shown that the solution to each problem corresponds to the \(n^{th}\) Catalan number. In order to manipulate these numbers in an easier way, there is a generating function which is used for calculating the general number of the sequence. Finally, there are shown some other interesting interpretations of Catalan’s numbers.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:382437
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in teaching
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2022-07-19 11:21:32