Dažas neatrisinātas problēmas kombinatoriskajā ģeometrijā
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Latvijas Universitāte
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Abstract
Maģistra darbā risinātas dažas kombinatoriskās ģeometrijas problēmas par tetradiem un pakošanas problēma ar V-pentakubiem. Šo problēmu risināšanai ir izstrādātas speciālas datorprogrammas un iegūti vairāki jauni rezultāti: ir atrasti visi tetradi no polimino, kuru laukums nepārsniedz 60; iegūti paralēlskaldņu n x n x 1, n < 21, un 5 x 5 x 5 blīvākie pakojumi no V-pentakubiem.
Atslēgvārdi: n-mino, pakošana, pentakubs, polimino, tetrads.
This Master thesis deals with some problems of combinatorial geometry on tetrads and packing problem with V-pentacubes. The special computer programmes have been elaborated for solving these problems, and several new results have been obtained: all polyominoes tetrads with area not exceeding 60 have been found, the densest packing of parallelepipeds n x n x 1, n < 21, and 5 x 5 x 5 have been obtained. Keywords: n-omino, packing, pentacube, polyomino, tetrad.
This Master thesis deals with some problems of combinatorial geometry on tetrads and packing problem with V-pentacubes. The special computer programmes have been elaborated for solving these problems, and several new results have been obtained: all polyominoes tetrads with area not exceeding 60 have been found, the densest packing of parallelepipeds n x n x 1, n < 21, and 5 x 5 x 5 have been obtained. Keywords: n-omino, packing, pentacube, polyomino, tetrad.