Catalanovi brojevi i njihovi rastavi

master's thesis

• Author: Ivana Iveković
• Mentor: Tomislav Došlić (mentor)
• Committee member: Tomislav Došlić (predsjednik povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-02-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Catalanov niz brojeva je cjelobrojni niz kombinatornog karaktera. Osim što se pojavljuju kao niz u mnogim područjima kombinatornih objekata, među kojima su poznatiji particije poligona na trokute, binarno sastavljanje zagrada (n + 1)-članih izraza, šetnja po cjelobrojnoj mreži, Dyckovi putevi, problem binarnih stabala, također se manifestiraju na mnogo neočekivanih mjesta. U ovom radu opisali smo njihova pojavljivanja te pokazali razne bijekcije s drugim kombinatornim objektima. Također smo pokazali više primjera njihovih trokutastih prikaza te proučavali svojstva dobivenih trokuta. Rad smo zaključili kombinatornim interpretacijama Catalanovih brojeva.

Abstract (english)

Catalan sequence of numbers is integer sequence with combinatorial context. It occurs as sequence in many widely studied classes of combinatorial objects such as the partitioning of a polygon into triangles, the binary bracketing of n + 1 terms, integral lattice walks, Dyck’s paths, problem of binary trees etc. Furthermore, they appear in a lot of unexpected places. In this paper we described their manifestation and presented bijections with different combinatorial objects. We also presented various triangle representations of Catalan numbers and studied properties of this triangles. Finally, we introduced some combinatorial interpretations of these numbers.

• Keywords: niz brojeva; particije poligona na trokute; binarno sastavljanje zagrada (n+1)-članih izraza; šetnja po cjelobrojnoj mreži; Dyckovi putevi; problem binarnih stabala; Catalanovi brojevi
• Keywords (english): integer sequence; partitioning of a polygon into triangles; the binary bracketing of n+1 terms; integral lattice walks; Dyck’s paths; problem of binary trees; Catalan numbers
• Language: croatian
• URN:NBN: urn:nbn:hr:217:433189
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-01-30 14:15:25