Nepristrane kombinatorne igre

undergraduate thesis

• Title (english): Impartial combinatorial games
• Author: Luka Tomić
• Mentor: Anamari Nakić (mentor)
• Committee member: Anamari Nakić (predsjednik povjerenstva)
• Committee member: Domagoj Kovačević (član povjerenstva)
• Committee member: Iva Manojlović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2023-07-12, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Ovaj završni rad bavi se nepristranim kombinatornim igrama, njihovom matematičkom teorijom uz navođenje nekoliko primjera tih igara, s naglaskom na Wythoffovoj igri koja je modifikacija nepristrane igre nim. U svom sadržaju iznosi i na temelju primjera predočuje matematički opis detalja vezanih za kombinatornu teoriju igara. Rad obrađuje i nekoliko poznatih nepristranih kombinatornih igara kao što su nim, sprouts, chomp, i Wythoffova igru, iznoseći neke detalje oko njihovih teoretskih podloga. Za Wythoffovu igru je osim matematičkih formalizama predstavljena interaktivna aplikacija Wythoff’s game koja korisniku nudi mogućnost igranja ove igre i pronalaženja pobjedničke strategije.

Abstract (english)

This baccalaureus graduate thesis deals with impartial combinatorial games, their
mathematical theory, showing several examples of these games, with an emphasis on
Wythoff’s game, which is a modification of the impartial game called nim. In its
content, based on examples, it presents a mathematical description of details related to
combinatorial game theory. This thesis is also covered by several well-known impartial
combinatorial games such as nim, sprouts, chomp, and Wythoff’s game, presenting
some details about their theoretical foundations. For Wythoff's game, along with mathematical formalisms, is shown an interactive application Wythoff's game which offers user to play this game, and to find winning strategy.

• Keywords: strategija; kombinatorne igre; standardne igre; P-pozicije; N-pozicije; suma igara; ishodi; opcije; nim-suma; nimber; graf; čvorovi; zlatni rez
• Keywords (english): strategy; combinatorial games; normal games; P-positions; N-positions; sum of games; outcomes; options; nim sum; nimber; graph; nodes; golden ratio
• Language: croatian
• URN:NBN: urn:nbn:hr:168:815573
• 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: 2023-10-11 10:47:57