Funkcije izvodnice u kombinatorici

master's thesis

• Author: Monika Režak
• Mentor: Boris Širola (mentor)
• Committee member: Boris Širola (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-03-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu govorimo o funkcijama izvodnicama i njihovoj primjeni pri određivanju eksplicitne formule za opći član niza. Na samom početku dajemo jedan motivacijski primjer u kojem je potrebno odrediti formulu za opći član niza gdje uvodimo i definiramo običnu funkciju izvodnicu. Nadalje, popisujemo sve popratne teoreme koje primjenjujemo u raznim primjerima kombinatoričkih problema. Na isti način uvodimo eksponencijalnu funkciju izvodnicu. Na kraju promatramo funkciju izvodnicu u teoriji brojeva te pomoću nje dolazimo do rekurzivne formule za Bernoullijeve brojeve.

Abstract (english)

In this graduate thesis we are talking about generating functions and their use with determining the explicit formula for the general sequence member. Right at the beginning we will show a motivational example in which it’s necessary to determine the general formula for the general sequence member where we introduce and define the ordinary generating function. Furthermore, we will describe all following theorems which will be applied in different examples of combinatorial problems. In the same way we will introduce the exponential generating function. At the end we will observe the generating function in number theory and use it to get to the recursive formula for Bernoulli numbers.

• Keywords: funkcija izvodnica; kombinatorika; Bernoullijevi brojevi
• Keywords (english): generating functions; combinatorics; Bernoulli numbers
• Language: croatian
• URN:NBN: urn:nbn:hr:217:160887
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2020-02-05
• Created on: 2019-09-05 09:09:57