Polimino ar uzdotu salikumu skaitu konstruēšanas problēma
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Latvijas Universitāte
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Abstract
Darbā aplūkota kombinatoriskās ģeometrijas problēma par tādu polimino konstruēšanu, kurus no uzdota k-mino kopijām var salikt tieši n veidos. Galvenā uzmanība pievērsta gadījumiem, kad k-mino lomā tiek ņemts domino un tetramino T. Atšķirībā no domino polimino eksistences problēma tetramino T gadījumā līdz šim nav atrisināta. Bakalaura darbā tā ir atrisināta visiem n <= 100, kā arī visiem Fibonači skaitļiem.
This work examines the problem of the combinatorial geometry on constructing such polyominoes which can be tiled from the prescribed k-omino copies exactly in n ways. The main attention has been paid to the cases when in the role of k-mino domino and tetromino T are taken. Unlike domino, the existence problem of polyomino in the case of tetromino T has not been solved yet. In this Bachelor thesis it has been solved for all n <= 100 as well as for all the Fibonacci numbers.
This work examines the problem of the combinatorial geometry on constructing such polyominoes which can be tiled from the prescribed k-omino copies exactly in n ways. The main attention has been paid to the cases when in the role of k-mino domino and tetromino T are taken. Unlike domino, the existence problem of polyomino in the case of tetromino T has not been solved yet. In this Bachelor thesis it has been solved for all n <= 100 as well as for all the Fibonacci numbers.