Dyckovi planinski putovi i Motzkinovi putovi

undergraduate thesis

• Title (english): Mountain Ranges and Motzkin Paths
• Author: Gabriel Matić
• Mentor: Andrea Aglić Aljinović (mentor)
• Committee member: Andrea Aglić Aljinović (predsjednik povjerenstva)
• Committee member: Domagoj Kovačević (član povjerenstva)
• Committee member: Kristijan Kilassa Kvaternik (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2018-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu obrađeni su Catalanovi, Motzkinovi i Narayanini brojevi, te Dyckovi putevi. Pokazali smo da su Catalanovi brojevi niz brojeva. Catalanove brojeve smo koristili kao uvod u Dyckove puteve, te Dyckov jezik. Pokazali smo kako je broj Dyckovih puteva duljine n jednak Catalanovom broju Cn.
Uveli smo i Naranayine brojeve koji određuju broj Dyckovih puteva duljine n s k vrhova. Zadnji pojam bili su Motzkinovi brojevi koji određuju broj istoimenih puteva. Uz to, napravljen je i računalni program koji računa i iscrtava Motzkinove i Dyckove puteve.

Abstract (english)

This paper is about Catalan, Motzkin and Narayana numbers, as well as Dyck paths. We have shown that Catalan numbers are a sequence. Catalan numbers have been used as an introduction to Dyck paths and the Dyck language. We have shown that the number of Dyck paths for a certain n is equal to the Catalan number Cn, and that the number of Dyck paths for a certain n with k peaks is equal to the Narayana number N(n, k). The last term we introduced was Motzkin numbers, which count the number of paths with the same name. In addition to that, a computer program has been written that counts and draws Motzkin and Dyck paths.

• Keywords: Kombinatorika; prebrojavanje; Dyckov jezik; Dyckovi putovi; planinski putovi; Motzkinovi putovi; Catalanovi brojevi; Narayanini brojevi; Java
• Keywords (english): Combinatorics; counting; Dyck language; Dyck paths; mountain ranges; Motzkin paths; Catalan numbers; Narayana numbers; Java
• Language: croatian
• URN:NBN: urn:nbn:hr:168:683132
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-13 22:50:28