# zbMATH — the first resource for mathematics

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
Full Text: