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master's thesis
Steinerove trojke i planiranje eksperimenata
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2024. urn:nbn:hr:168:571939
Hrelja, Mateo
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

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Hrelja, M. (2024). Steinerove trojke i planiranje eksperimenata (Master's thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:571939

Hrelja, Mateo. "Steinerove trojke i planiranje eksperimenata." Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2024. https://urn.nsk.hr/urn:nbn:hr:168:571939

Hrelja, Mateo. "Steinerove trojke i planiranje eksperimenata." Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2024. https://urn.nsk.hr/urn:nbn:hr:168:571939

Hrelja, M. (2024). 'Steinerove trojke i planiranje eksperimenata', Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 31 December 2024, https://urn.nsk.hr/urn:nbn:hr:168:571939

Hrelja M. Steinerove trojke i planiranje eksperimenata [Master's thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2024 [cited 2024 December 31] Available at: https://urn.nsk.hr/urn:nbn:hr:168:571939

M. Hrelja, "Steinerove trojke i planiranje eksperimenata", Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:168:571939

Metadata
TitleSteinerove trojke i planiranje eksperimenata
Title (english)Steiner triplets and experiment planning
AuthorMateo Hrelja
MentorAnamari Nakić (mentor)
Committee memberAnamari Nakić (predsjednik povjerenstva)
Committee memberAndrea Aglić Aljinović (član povjerenstva)
Committee memberDomagoj Kovačević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2024-07-03, Croatia
Abstract
Steinerova trojka (V, B) je kombinatorni dizajn koji se sastoji od v-članog skupa točaka V i skupa tročlanih blokova B, uz uvjet da se svaki par iz V pojavljuje u točno jednom bloku iz B. Steinerove trojke STS(v) postoje ako i samo ako v ≡ 1, 3 (mod 6). U ovom radu, opisana su svojstva i dokazani uvjeti egzistencije Steinerovih trojki, prikazane metode njihove konstrukcije i dan osvrt na težak problem određivanja izomorfizma i klasifikacije Steinerovih trojki. Opisani su Latinski kvadrati te simetrične idempotentne kvazigrupe i simetrične polu-idempotentne kvazigrupe. Ove strukture su neophodne za Boseovu konstrukciju i modificiranu Skolemovu konstrukciju Steinerovih trojki. Boseova konstrukcija koristi pritom idempotentnu kvazigrupu, dok Skolemova konstrukcija koristi polu-idempotentnu kvazigrupu. Istražen je pojam izomorfizma Steinerovih trojki. Opisan je otvoren problem enumeracije i klasifikacije Steinerovih trojki. Prikazana je primjena Steinerovih trojki u planiranju eksperimenata, te je opisana implementirana aplikacija koja koristi Steinerove trojke za efikasno planiranje izvođenja eksperimenata.
Abstract (english)
A Steiner triple system (V, B) is a combinatorial design consisting of a set V of v points and a set B of three-element blocks, with the condition that each pair from V appears in exactly one block from B. Steiner triple systems STS(v) exist if and only if v ≡ 1, 3 (mod 6). In this paper, the properties and existence conditions of Steiner triple systems are described, methods of their construction are presented, and an overview is given of the challenging problem of determining isomorphism and classification of Steiner triple systems. Latin squares, as well as symmetric idempotent quasigroups and symmetric half-idempotent quasigroups, are described. These structures are necessary for Bose’s construction and the modified Skolem construction of Steiner triple systems. Bose’s construction uses an idempotent quasigroup, while Skolem’s construction uses a half-idempotent quasigroup. The concept of isomorphism of Steiner triple systems is explored. The open problem of enumeration and classification of Steiner triple systems is described. A practical application of Steiner triple systems in experiment design and planning is presented, and an implemented web-application that uses Steiner triple systems for efficient experimental planning is described.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:571939
Study programmeTitle: Computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
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Created on2024-10-12 20:49:11