o:17882 Primena Grebnerovih baza na probleme popločavanja doktorska disertacija Application of the Grobner bases theory to tiling problems : doctoral dissertation sr Predmet ove doktorske disertacije je primena algebarskih tehnika na jednu od centralnih tema kombinatorike i diskretne geometrije - poliomino poplocavanja. Poliomino poplocavanja su interesantna ne samo matematicarima nego i zicarima i biolozima, a imaju i primenu u racunarskim naukama. U ovoj disertaciji akcenat je stavljen na mogucnost da se posebna klasa problema poplocavanja koja su invarijantna u odnosu na delovanje konacne grupe resi primenom teorije Grebnerovih baza za prstene polinoma nad prstenom celih brojeva Z. Metoda koja se koristi odrazava duboku povezanost izmedu algebre, geometrije i kombinatorike... Subject of this doctoral thesis is the application of algebraic techniques on one of the central topics of combinatorics and discrete geometry - polyomino tiling. Polyomino tilings are interesting not only to mathematicians, but also to physicists and biologists, and they can also be applied in computer science. In this thesis we put some emphasis on possibility to solve special class of tiling problems, that are invariant under the action of nite group, by using theory of Grobner basis for polynomial rings with integer coecients. Method used here re ects deep connection between algebra, geometry and combinatorics... Matematika - Algebra / Mathemetics - Algebra Datum odbrane: 26.07.2017. Z-poplocavanja, simetricna Z-poplocavanja, Grebnerove baze, resetkeu ravni, prsten invarijanti Z-tilings, symmetric Z-tilings, Gobner bases, lattice in the plane, ring ofinvariants yes 50180111 91552101 5894 91552100 50180111 2018-07-12T12:05:22.053Z 45 no 46 mentor Manuela, 1975- Muzika-Dizdarević 2017 63 mentor Rade, 1954- Živaljević 2017 63 član komisije Aleksandar, 1955- Lipkovski 2017 63 član komisije Siniša, 1954- Vrećica 2017 63 član komisije Zoran, 1965- Petrović 2017 63 član komisije Branislav. Prvulović 2017 83 lista 33233659 http://phaidrabg.bg.ac.rs/o:17882 no yes 2 2018-07-12T12:05:22.320Z 70 11 1066609 1066619 1066622 Z-poplocavanja, simetricna Z-poplocavanja, Grebnerove baze, resetkeu ravni, prsten invarijanti Z-tilings, symmetric Z-tilings, Gobner bases, lattice in the plane, ring ofinvariants 1738 11A31 2017