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Succession rules and Deco polyominoes

Published online by Cambridge University Press:  15 April 2002

Elena Barcucci ,
Sara Brunetti  and
Francesco Del Ristoro
Elena Barcucci
Affiliation:
Dipartimento di Sistemi e Informatica, Via Lombroso 6/17, 50134 Firenze, Italy; (barcucci@dsi.unifi.it)
Sara Brunetti
Affiliation:
Dipartimento di Sistemi e Informatica, Via Lombroso 6/17, 50134 Firenze, Italy; (brunetti@dsi.unifi.it)
Francesco Del Ristoro
Affiliation:
Dipartimento di Sistemi e Informatica, Via Lombroso 6/17, 50134 Firenze, Italy; (fdr@dsi.unifi.it)
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Abstract

In this paper, we examine the class of "deco" polyominoes and the succession rule describing their construction. These polyominoes are enumerated according to their directed height by factorial numbers. By changing some aspects of the "factorial" rule, we obtain some succession rules that describe various "deco" polyomino subclasses. By enumerating the subclasses according to their height and width, we find the following well-known numbers: Stirling numbers of the first and second kind, Narayana and odd index Fibonacci numbers. We wish to point out how the changes made on the original succession rule yield some new succession rules that produce transcendental, algebraic and rational generating functions.

Keywords

Polyominoenumerationsuccession rulegenerating function combinatorial interpretation.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 1 , January 2000 , pp. 1 - 14
Copyright
© EDP Sciences, 2000

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References

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