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master's thesis
Stirlingovi polinomi
2019. urn:nbn:hr:126:184063
Majić, Monika
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science

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Majić, M. (2019). Stirlingovi polinomi (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:184063

Majić, Monika. "Stirlingovi polinomi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:184063

Majić, Monika. "Stirlingovi polinomi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:184063

Majić, M. (2019). 'Stirlingovi polinomi', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:184063

Majić M. Stirlingovi polinomi [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:126:184063

M. Majić, "Stirlingovi polinomi", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:184063

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Metadata
TitleStirlingovi polinomi
Title (english)Stirling Polynomials
AuthorMonika Majić
MentorIvica Martinjak (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberIvica Martinjak (član povjerenstva)
Committee memberDomagoj Ševerdija (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
Osijek
Defense date and country2019-07-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Discrete and Combinatorial Mathematics
Abstract
U ovom radu obrađujemo Stirlingove polinome kao jednu od familija polinoma koja se pojavljuje u kombinatornoj matematici. Stirlingovi polinomi su usko povezani sa Stirlingovim brojevima. U radu prvo predstavljamo binomni koeficijent i najbitnija svojstva. Nakon toga upoznajemo se s pojmom Fibonaccijevi brojevi i njihovom relacijom s Pascalovim trokutom. Sljedeća bitna stavka koju smo obradili jesu funkcije izvodnice te navodimo primjer funkcije izvodnice za Fibbonaccijev niz brojeva. Kao jednu od glavnih tema uvodimo specijalne brojeve s naglaskom na Stirlingove brojeve prve i druge vrste te njihovom vezom s nekim specijalnim brojevima. Poseban zadatak je bio definiranje Stirlingovih polinoma, prvo konvolucijskih, zatim Stirlingovih polinoma koje je definirao R. P. Stanley i na kraju Stirlingovih polinoma koji su Shefferov niz te predstavljaju specijalan slučaj generaliziranih Bernoullijevih polinoma.
Abstract (english)
In this paper we analyze Stirling polynomials as one of the polynomial families that appears in combinatorial mathematics. Stirling polynomials are closely related to Stirling numbers. In the paper we first present the binomial coefficient and its most important properties. After that, we get to know the term Fibonacci numbers and their relation to Pascal triangle. The next important theme we learn about are the generating functions, and we give an example of the generating function for the Fibbonacci series of numbers. One of the main themes is introducing special numbers with an emphasis on Stirling numbers of the first and second kind and their connection with some special numbers. A special task was to define Stirling polynomials, first convolutional, then Stirling polynomials defined by R. P. Stanley and at the end Stirling polynomials which are Sheffer sequence and represent a special case of generalized Bernoulli polynomials.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:184063
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-07-08 09:52:32