Catalanov problem

undergraduate thesis

• Title (english): Catalan problem
• Author: Marko Sertić
• Mentor: Andrea Aglić-Aljinović (mentor)
• Committee member: Andrea Aglić Aljinović (predsjednik povjerenstva)
• Committee member: Mario Krnić (član povjerenstva)
• Committee member: Ana Žgaljić Keko (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Ovaj rad bavi se analizom Catalanovog problema i Catalanovih brojeva. Na samom početku rada dana je definicija Catalanovog problema. Zatim je pokazan izvod funkcije izvodnice n-tog Catalanovog broja kao i izvod eksplicitne vrijednosti n-tog Catalanovog broja. Također je u radu opisano i asimptotsko ponašanje Catalanovih brojeva, te su navedena određena svojstva Catalanovih brojeva. U nastavku su također navedena i neka od kombinatornih interpretacija Catalanovih brojeva. Osim samog opisa interpretacija, dan je i matematički dokaz koji potvrđuje da su rješenja svih interpretacija Catalanovi brojevi. Za kraj samog rada obrađena je i programska interpretacija Catalanovih brojeva. Dani su algoritmi rješavanja određenih problema, kao i uputstva za korištenje aplikacije.

Abstract (english)

This work deals with the problems and analysis of Catalan numbers. The definition of Catalan problem is defined at the very beginning of this document. A mathematical proof of generating functions of n-th Catalan number as well as the extract of the explicit value of the n-th Catalan number is given. The asymptotic behavior of Catalan numbers is also described, and certain properties of them are given. The combinatorial interpretation of Catalan numbers is also listed at the following. Beside the description of interpretations, the mathematical proof that confirms the solutions of all interpretation are Catalan numbers, is given too. The work treated and programatic interpetated Catalan numbers in the end. Algorithms that solve certain problems as well as the instructions for using the application are shown and presented

• Keywords: Catalanov problem; Catalanovi brojevi; Asimptotsko ponašanje Catalanovih brojeva; Kombinatorne interpretacije Catalanovih brojeva
• Keywords (english): Catalan problem; Catalan numbers; Asymptotic behavior of Catalan numbers; Combinatorial interpretation of Catalan numbers
• Language: croatian
• URN:NBN: urn:nbn:hr:168:408255
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2018-02-05 17:54:17