Polyominoes defined by two vectors

Polyominoes defined by two vectors

The polyominoes' problem defined by two vectors has been proposed by M. Nivat in the course of the seminar held at the Dipartimento di Sistemi e Informatica di Firenze, on September 1992, on the subject Tiling the plane with a horizontal bar h m and a vertical bar v n . It is the problem of est...

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Veröffentlicht in:Theoretical computer science 1994-01, Vol.127 (1), p.187-198
1. Verfasser: Del Lungo, A.
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Sprache:eng
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Applied sciences
Artificial intelligence
Computer science
control theory
systems
Exact sciences and technology
Problem solving, game playing
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description The polyominoes' problem defined by two vectors has been proposed by M. Nivat in the course of the seminar held at the Dipartimento di Sistemi e Informatica di Firenze, on September 1992, on the subject Tiling the plane with a horizontal bar h m and a vertical bar v n . It is the problem of establishing the existence of a polyomino with a given number of cells in every column and every row. The problem is solved for the following classes of polyominoes: directed column-convex, directed convex, and parallelogram. The problem is also solved in the class of convex polyominoes in a particular case. Furthermore, it is possible to define an algorithm that controls the existence of a directed column-convex, or directed convex, or parallelogram polyomino, with a given number of cells in every column and in every row.
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subjects Applied sciences
Artificial intelligence
Computer science
control theory
systems
Exact sciences and technology
Problem solving, game playing
title Polyominoes defined by two vectors
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