prikaz prve stranice dokumenta Rastavljivi dizajni
  Download
PDF 549.77 KB
master's thesis
Rastavljivi dizajni
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:540972
Marković, Ilija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Marković, I. (2015). Rastavljivi dizajni (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:540972

Marković, Ilija. "Rastavljivi dizajni." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:540972

Marković, Ilija. "Rastavljivi dizajni." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:540972

Marković, I. (2015). 'Rastavljivi dizajni', Master's thesis, University of Zagreb, Faculty of Science, accessed 16 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:540972

Marković I. Rastavljivi dizajni [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 May 16] Available at: https://urn.nsk.hr/urn:nbn:hr:217:540972

I. Marković, "Rastavljivi dizajni", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:540972

Metadata
TitleRastavljivi dizajni
AuthorIlija Marković
MentorVedran Krčadinac (mentor)
Committee memberZvonimir Tutek (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberVedran Krčadinac (član povjerenstva)
Committee memberBoris Guljaš (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Motivacija za pisanje diplomskog rada bila je Kirkmanov problem 15 učenica. Jedna od interpretacija tog problema je rastavljivi dizajn. Na početku smo se upoznali s dizajnima i iznijeli osnovne rezultate koji vrijede za dizajne. Generalizacija dizajna je u parovima balansirani dizajn (PBD). Na toj incidencijskoj strukturi definiramo pojam rastavljivosti. Jedan nuždan uvjet za postojanje dizajna je Fisherova nejednakost. Dizajni koji dostižu Fisherovu nejednakost su simetrični dizajni. Za rastavljive dizajne vrijedi poboljšanje te nejednakosti, Boseova nejednakost. Nama su posebno zanimljivi dizajni koji dostižu Boseovu nejednakost. To su afino rastavljivi dizajni. Koristeći afino rastavljive dizajne možemo konstruirati simetrične dizajne. Na kraju diplomskog rada povezali smo rastavljive dizajne s još jednom zanimljivom strukturom, ekvidistantnim kodovima.
Abstract (english)
Kirkman’s schoolgirl problem motivated the writing of this graduate work. It is a famous example of a resolvable design. At the beginning we made an introduction to designs and gave some basic results that apply to designs. The incidence structure on which we define the notion of resolution is pairwise balanced design (PBD). One necessary condition for the existence of a design is Fisher’s inequality. Designs that attain the equality in Fisher’s inequality are symmetric designs. If a PBD admits a resolution, a stronger result known as Bose’s inequality holds. We are interested in designs attaining the equality in Bose’s inequality. These are affine resolvable designs. We can construct symmetric designs using affine resolvable designs. In the end we explored the connections between equidistant codes and resolvable designs.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:540972
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-22 11:56:37