Specijalni nizovi

undergraduate thesis

• Title (english): Special Sequences
• Author: Rut Pušelj
• Mentor: Andrea Aglić-Aljinović (mentor)
• Committee member: Andrea Aglić Aljinović (predsjednik povjerenstva)
• Committee member: Mario Osvin Pavčević (član povjerenstva)
• Committee member: Lana Horvat Dmitrović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2016-07-11, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Specijalni nizovi često se pojavljuju u diskretnoj matematici. Za Fibonaccijeve, Lucasove, Catalanove, Bernoullijeve, Eulerove i Ramseyeve brojeve, koji su dobili ime po osobama koje su ih prve otkrile, dane su definicije, svojstva, rekurzivne relacije i funkcije izvodnice. Opisani su najvažniji kombinatorički problemi u kojima se ti brojevi pojavljuju. Navedeni su primjeri njihovog pojavljivanja, radi lakše vizualizacije, unutar ostalih područja znanosti, umjetnosti, tehnologija i unutar struktura živog i neživog svijeta u prirodi.

Abstract (english)

Special sequences are a frequent occurrence in the field of discrete mathematics.
For certain numbers that were named after the people who introduced them
into mathematics, i.e. for Fibonacci, Lucas, Catalan, Bernoulli, Eulerian and
Ramsey numbers, their belonging definitions, properties, recurrence relations and
generating functions are introduced in this paper. Furthermore, most frequent
problems in combinatorics using the listed numbers are described. Also, there are
examples describing their occurrences in other scientific fields besides mathematics,
art, technology and inside all forms of nature, for better understanding purposes.

• Keywords: Fibonaccijevi brojevi; Lucasovi brojevi; Catalanovi brojevi; Bernoullijevi brojevi; Eulerovi brojevi; Ramseyevi brojevi; rekurzivna relacija; funkcija izvodnica
• Keywords (english): Fibonacci numbers; Lucas numbers; Catalan numbers; Bernoulli numbers; Eulerian numbers; Ramsey numbers; recurrence relation; generating function
• Language: croatian
• URN:NBN: urn:nbn:hr:168:431724
• 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: 2018-02-06 11:28:24