20.500.12556/RUL-165073 Bellovi polinomi Bell polynomials Bellovi polinomi so pomemben matematični pojem v kombinatoriki, ki se uporablja za štetje različnih načinov razdelitve množice v neprazne podmnožice. Prvi jih je podrobneje opisal škotski matematik Eric Temple Bell. V tej nalogi raziščemo osnovne lastnosti Bellovih polinomov in prikažemo nekaj zanimivih primerov. Velik del naloge je posvečen raziskovanju povezav Bellovih polinomov z različnimi kombinatoričnimi števili, kot so Bellova, Stirlingova, Lahova in idempotentna števila. Izpeljanih je nekaj zanimivih rekurzivnih zvez, na koncu pa je prikazano še, kako lahko Bellove polinome uporabimo v Faà di Brunovi formuli. Cilj naloge je bralcu predstaviti raznolikost Bellovih polinomov ter njihov pomen v kombinatoriki in širši matematični teoriji. Bell polynomials are an important mathematical concept in combinatorics, used for counting different ways of partitioning a set into non-empty subsets. They were first described in detail by the Scottish mathematician Eric Temple Bell. In this thesis, we explore the fundamental properties of Bell polynomials and present some interesting examples. A significant part of the thesis is dedicated to examining the connections between Bell polynomials and various combinatorial numbers, such as Bell numbers, Stirling numbers, Lah numbers, and idempotent numbers. Several intriguing recursive relations are derived, and finally, it is shown how Bell polynomials can be applied in Faà di Bruno's formula. The goal of this thesis is to introduce the reader to the diversity of Bell polynomials and their importance in combinatorics and broader mathematical theory. kombinatorika Bellovi polinomi Stirlingova števila Lahova števila idempotentna števila Faà di Brunova formula combinatorics Bell polynomials Stirling numbers Lah numbers idempotent numbers Faà di Bruno's formula true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2024-11-22 11:00:01 2024-11-22 11:00:08 2024-12-06 10:42:29 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 37294 217970691 Matkovic_Antea_maris_-_Bellovi_polinomi.pdf Matkovic_Antea_maris_-_Bellovi_polinomi.pdf 1 F51C05E9F785D13A5D588A9E5EABEC96 a778c9a223b50a2c15b5ae47b8d1b0d9c75aa645fe2f705c68e9dd33e1668e5a 2846ad59-a8b8-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=196026 Fakulteta za računalništvo in informatiko 0 0 0