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master's thesis
Johnsonova shema
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:887584
Šupe, Katarina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Šupe, K. (2021). Johnsonova shema (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:887584

Šupe, Katarina. "Johnsonova shema." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:887584

Šupe, Katarina. "Johnsonova shema." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:887584

Šupe, K. (2021). 'Johnsonova shema', Master's thesis, University of Zagreb, Faculty of Science, accessed 01 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:887584

Šupe K. Johnsonova shema [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 November 01] Available at: https://urn.nsk.hr/urn:nbn:hr:217:887584

K. Šupe, "Johnsonova shema", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:887584

Metadata
TitleJohnsonova shema
Title (english)Johnson's scheme
AuthorKatarina Šupe
MentorVedran Krčadinac (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberLuka Grubišić (član povjerenstva)
Committee memberSlaven Kožić (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Neka je \(V\) skup od \(v\) elemenata i \(\Omega = \binom{V}{k}\) familija svih \(k\)-članih podskupova od \(V\) . Johnsonov graf \(J(v,k,i) \) ima \(\Omega\) kao skup vrhova, a dva vrha su susjedna ako se sijeku u \(k-i\) elemenata. Johnsonovi grafovi imaju zanimljiva svojstva koja ih čine asocijacijskom shemom. Skup koji sadrži grafove \(G_i = J(v,k,i) \), \(i= 0,\dots, k\) nazivamo Johnsonovom shemom i označavamo s \(J(v,k) \). U ovom radu promatramo vezu između Johnsonovih grafova i dizajna, uz pomoć koje dokazujemo Ray-Chaudhurijev i Wilsonov teorem. Na kraju izvodimo parametre Johnsonove sheme i dokazujemo Delsarteov teorem koji povezuje dizajne sa svojstvenim potprostorima Johnsonove sheme.
Abstract (english)
Let \(V\) be a set of \(v\) points and let \(\Omega = \binom{V}{k}\) the set of all \(k\)-subsets of \(V\) . The Johnson graph \(J(v,k,i) \) has \(\Omega\) as vertex set and two vertices are adjacent if they intersect in exactly \(k-i\) points. Johnson graphs have interesting properties that make them an association scheme. The set consisting of \(G_i = J(v,k,i) \), \(i= 0,\dots, k\) is called Johnson scheme and denoted by \(J(v,k) \). In this thesis we explore the relationship between Johnson graphs and designs, with the help of which we prove Ray-Chaudhuri and Wilson's theorem. In the end, we determine parameters of the Johnson scheme and prove Delsarte's theorem, connecting designs with eigenspaces of the Johnson scheme.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:887584
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-11-09 09:54:19