Sprague-Grundyjeva teorija nepristranih kombinatornih igara

master's thesis

• Author: Iva Madjerčić
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Goran Muić (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-11, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics; Other Mathematical Disciplines

Abstract

Ovaj rad daje kratki pregled teorije nepristranih kombinatornih igara. Osnovni obrađeni koncepti i rezultati su: klasifikacija pozicija kao pobjedničkih za prvog, odnosno drugog igrača, definicija Sprague-Grundyjeve funkcije, dokaz istoimenog teorema, primjena teorije na rješavanje igara Nim i Hackenbush te analiza igre Chomp korištenjem računala. Općenita teorija je detaljno ilustrirana na velikom broju primjera kombinatornih igara, od nekih dobro poznatih i često igranih do onih izmišljenih samo za potrebe ovog rada.

Abstract (english)

This paper gives a brief overview of impartial combinatorial games. The main concepts and results are as follows: classification of positions as winning for the first, and second player, definition of Sprague-Grundy’s function, the proof of homonymous theorem, application of theory on solving Nim and Hackenbush games and the analysis of the game of Chomp by using the computer. The basic theory is illustrated in detail on a variety of examples of combinatorial games, ranging from some well known and often used to the ones invented for the purpose of this paper.

• Keywords: teorija nepristranih kombinatornih igara; Sprague-Grundyjeva teorija
• Keywords (english): theory of impartial combinatorial games; Sprague-Grundy's theory
• Language: croatian
• URN:NBN: urn:nbn:hr:217:904605
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-14 11:31:49