20.500.12556/RUL-95870 Catalanova števila magistrsko delo V delu predstavimo nekatere kombinatorične probleme, ki ustrezajo zaporedju Catalanovih števil, ter zapišemo bijekcije med njimi. Podamo eksplicitno formulo in rekurzivno zvezo za izračun splošnega člena v tem zaporedju in ju dokažemo na več načinov. Izpeljemo rodovno funkcijo zaporedja ter si ogledamo asimptotiko Catalanovih števil. Definiramo $k$-Catalanova števila kot eno izmed posplošitev in opišemo kombinatorične probleme, ki jim ustrezajo. Dokažemo tudi posplošeno formulo, ki ustreza $k$-Catalanovim številom, in na kratko omenimo še nekaj zgodovinskih animivosti. The aim of this thesis is to present some examples of combinatorial problems that correspond to the sequence of Catalan numbers and write down bijections between them. We give an explicit formula and a recurrence relation for computation of the general term of this sequence and find different proofs that they hold. We derive the formula for the generating function of the sequence and take a look at asymptotic behavior of Catalan numbers. We define $k$-Catalan numbers as an example of a generalization and describe the corresponding combinatorial problems. We also prove the generalized formula that corresponds to $k$-Catalan numbers and briefly mention a few interesting historical facts. Catalanova števila preštevalna kombinatorika bijekcije Dyckove poti Catalan numbers enumerative combinatorics bijections Dyck paths true false false [L. Kozarski] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2017-09-22 09:53:24 2017-09-22 09:53:24 2022-08-10 06:59:44 0000-00-00 00:00:00 2014 0 Ljubljana 2014 Ljubljana 66 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.1 17207641 RAZ_Kozarski_Lara_i2014.pdf RAZ_Kozarski_Lara_i2014.pdf 1 8296B9758EC7EFEB950E78E87DA2BD3C d0d21f4e831783c5612a1049bbd02be9915433d60815a22c8b3fc543377aa47c da6a1fbe-a1b3-11eb-a523-00155dcfd717 20.500.12556/rul/531398f8-e045-42fc-9d79-7394030bf6d9 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=104518 Fakulteta za matematiko in fiziko 0 0 0