Algebraic Languages and Polyominoes Enumeration

Abstract In this paper, the use of algebraic languages theory in solving an open problem in combinatorics is shown. By constructing a bijection between convex polyominoes and words of an algebraic language, and by solving the corresponding algebraic system, we prove that the number of convex polyominoes with perimeter 2n + 8 is (2n + 11)4 n −4(2n + 1)( 2n n ) .

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