Latinski kvadrati

undergraduate thesis

• Title (english): Latin Squares
• Author: Luka Banić
• Mentor: Anamari Nakić (mentor)
• Committee member: Anamari Nakić (predsjednik povjerenstva)
• Committee member: Marina Furkes (član povjerenstva)
• Committee member: Filip Martinović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2022-07-01, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovome radu uvodi se matematički objekt latinskih kvadrata te odgovarajuća svojstva i problemi. Kratko se objašnjava njihova primjena kroz povijest te razvoj u znanost o latinskim kvadratima. Daje se pregled osnovnih svojstava latinskih kvadrata te uvode pojmovi transpozicije, transverzale, reduciranosti, konjugacije, idempotentnosti i ortogonalnosti latinskih kvadrata. Na temelju navedenih svojstava vrše se različite klasifikacije u odgovarajuće razrede latinskih kvadrata. Pobliže se opisuje pojam parcijalnih latinskihi kvadrata i kritičnih skupova te se uvodi problem njihove konstrukcije i klasifikacije. Na temelju znanja o svojstvima i konstrukciji latinskih kvadrata te odgovarajućih kritičnih skupova, korištenjem jezika HTML, CSS i JavaScript, izrađena je interaktivno-edukativna web-aplikacija za nadopunjavanje parcijalnih latinskih kvadrata.

Abstract (english)

In this thesis, the Latin sqaure and the corresponding properties and problems are introduced as mathematical objects. Their application throughout history and the development into a science of latin squares is briefly explained. An overview of the basic properties of Latin squares is given and the concepts of transposition, transversal, reduction, conjugation, idempotence and orthogonality of latin squares are introduced. Based on the aformentioned properties, different classifications to the corresponding classes of latin squares are presented. The notion of partial latin squares and critical sets is described in more detail and the problem of their construction and classification is introduced. Based on knowledge of the properties and constructions of Latin squares and the corresponding critical sets, using the languages HTML, CSS and JavaScript, an interactive-educational web application for completing partial Latin squares is created.

• Keywords: latinski kvadrat; parcijalni latinski kvadrat; web-aplikacija; algoritam
• Keywords (english): latin square; partial Latin square; web-application; algorithm
• Language: croatian
• URN:NBN: urn:nbn:hr:168:745910
• 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: 2023-01-15 09:44:09