Družabna igra SET in problem največjega krova

diplomsko delo

Jožef Ilija (Author), Aleš Vavpetič (Mentor)

Abstract

Družabna igra SET je igra s kartami. Osnovni element igre so karte z različnimi lastnostmi, med katerimi išcemo po tri, ki izpolnjujejo SET pravilo. Problem največjega krova išce največjo možno podmnožico afinega prostora Z_3^n v odvisnosti od n, znotraj katere ne obstajajo trije kolinearni elementi. Problem se za primer n = 4 lahko predstavi s SET kartami tako, da išcemo čim večje število kart, med katerimi nobene tri ne izpolnjujejo SET pravila. Naloga razišce in obravnava nekatere preproste pristope za reševanje problema najvčjega krova za poljuben n z uporabo kombinatoričnih in števnih argumentov. Rezultat je metoda štetja hiperravnin, s katero določimo zgornje meje problema za dimenzije do n = 8 ter aplikacija za vizualizacijo afinih prostorov dimenzij n = 2,3,4.

Keywords

družabna igra SET;SET;problem največjega krova;afina geometrija;vizualizacija;metoda štetja hiperravnin;računalništvo;matematika;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2025
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[J. Ilija]
UDC:	004:51:793.5/.7(043.2)
COBISS:	227773443
Views:	96
Downloads:	753
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The card game SET and the cap set problem
Secondary abstract:	The SET card game consists of cards containing shapes with different prop erties. The goal of the game is to find sets of three cards that fulfill the SET rule. A cap set is a subset of the affine space Zn 3 where no three elements are collinear. The cap set problem explores the maximum possible size of cap sets with regards to the dimension n. In the particular case of n = 4 the affine space Z4 3 can be represented with the 81 cards that are contained within the SET card game. The cap set problem in this instance searches for the largest amount of cards possible, such that no three cards fulfill the SET rule. This thesis aims to explore and present some simple and easy to understand approaches for attempting to solve the cap set problem using counting arguments and combinatorics. The main result of the thesis is the hyperplane counting method, which gives us upper bounds for the problem in dimensions up to n = 8 as well as an application that helps visualize the considered affine spaces of dimensions n = 2,3,4 as well as their subsets.
Secondary keywords:	affine geometry;cap set problem;visualization;hyperplane counting method;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000407
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	1 spletni vir (1 datoteka PDF (40 str.))
ID:	25931568