20.500.12556/RUL-167399 Družabna igra SET in problem največjega krova The card game SET and the cap set problem 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. 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. afina geometrija problem največjega krova vizualizacija metoda štetja hiperravnin affine geometry cap set problem visualization hyperplane counting method true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2025-02-19 16:55:04 2025-02-19 16:55:12 2025-03-03 09:49:01 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 37634 227773443 Ilija_Jozef_-_Druzabna_igra_SET_in_problem_najvecjega_krova.pdf Ilija_Jozef_-_Druzabna_igra_SET_in_problem_najvecjega_krova.pdf 1 956605CED73799CE6E86B5B886B15FB3 10f0ab9bb64a127f96f1ac599bd347666f74abaeb9d5f1408bc8618c6d7ca6d6 03e54848-eed9-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=199793 Fakulteta za računalništvo in informatiko 0 0 0