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undergraduate thesis
Kombinatorne primjene i asimptotski razvoji Catalanovih brojeva
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2017. urn:nbn:hr:168:861623
Manović, Mato
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

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Manović, M. (2017). Kombinatorne primjene i asimptotski razvoji Catalanovih brojeva (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:861623

Manović, Mato. "Kombinatorne primjene i asimptotski razvoji Catalanovih brojeva." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2017. https://urn.nsk.hr/urn:nbn:hr:168:861623

Manović, Mato. "Kombinatorne primjene i asimptotski razvoji Catalanovih brojeva." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2017. https://urn.nsk.hr/urn:nbn:hr:168:861623

Manović, M. (2017). 'Kombinatorne primjene i asimptotski razvoji Catalanovih brojeva', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 28 June 2024, https://urn.nsk.hr/urn:nbn:hr:168:861623

Manović M. Kombinatorne primjene i asimptotski razvoji Catalanovih brojeva [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2017 [cited 2024 June 28] Available at: https://urn.nsk.hr/urn:nbn:hr:168:861623

M. Manović, "Kombinatorne primjene i asimptotski razvoji Catalanovih brojeva", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:168:861623

Metadata
TitleKombinatorne primjene i asimptotski razvoji Catalanovih brojeva
Title (english)Combinatorial Applications and Asymptotic Expansions of Catalan numbers
AuthorMato Manović
MentorTomislav Burić (mentor)
Committee memberTomislav Burić (predsjednik povjerenstva)
Committee memberLana Horvat Dmitrović (član povjerenstva)
Committee memberLenka Mihoković (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2017-07-10, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
Cilj prvog dijela ovog rada je bio pronaći i programski implementirati učestale kombinatorne probleme koji u svojoj osnovi imaju veze s Catalanovim brojevima.Neki od primjera takvih problema su putovi u cjelobrojnoj mreži, definiranje redoslijeda izvođenja operacija u algebarskom izrazu, permutacije uporabom stoga i mnogi drugi.Drugi dio rada se odnosi na dio numeričke matematike koja se bavi aproksimacijom funkcija korištenjem asimptotskog razvoja.U ovom radu za aproksimaciju Catalanovih brojeva korišten je Burić-Elezović asimptotski razvoj kvocijenta dviju gama funkcija budući da same Catalanove brojeve možemo izraziti preko kvocijenta dviju gama funkcija.Izračun koeficijenata asimptotskog razvoja Catalanovih brojeva bilo je potrebno implementirati u prikladnom matematičkom programskom alatu.
Abstract (english)
The goal of the first part of thesis was to find and programmatically implement frequent combinatorial problems whose basis is related with Catalan numbers. Some problem examples are lattice paths along the edges of the grid, defining the sequence of operations in algebraic expression and permutations using stack. The second part of thesis is about the segment of numerical mathematics used for approximation of functions by using asymptotic expansion. In this thesis, the Burić-Elezović asymptotic expansion of the quotioent of two gamma functions was used to approximate Catalan numbers as they can be expressed over the quotient of two gamma functions. Calculating the asymptotic expansion coefficients of Catalan numbers required implementation in suitable mathematical program tool.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:861623
Study programmeTitle: Computing
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
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Created on2019-03-13 22:36:58