Primena Grebnerovih baza na probleme popločavanja
Application of the Grobner bases theory to tiling problems.
Author
Muzika-Dizdarević, ManuelaMentor
Živaljević, Rade
Committee members
Lipkovski, AleksandarVrećica, Siniša
Petrović, Zoran
Prvulović, Branislav
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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 Gr obner basis for polynomial rings with integer coecients. Method
used here re
ects deep connection between algebra, geometry and combinatorics...