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Algebraic languages and polyominoes enumeration. (English) Zbl 0985.68516
Summary: We show the use of algebraic language theory in solving an open problem in combinatorics. 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 \((2n+11)4^n- 4(2n+1)\binom{2n}{n}\).

MSC:
68Q42 Grammars and rewriting systems
05B50 Polyominoes
68R05 Combinatorics in computer science
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