# Succession rules and Deco polyominoes

Elena Barcucci; Sara Brunetti; Francesco Del Ristoro

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 34, Issue: 1, page 1-14
- ISSN: 0988-3754

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topBarcucci, Elena, Brunetti, Sara, and Ristoro, Francesco Del. " Succession rules and Deco polyominoes." RAIRO - Theoretical Informatics and Applications 34.1 (2010): 1-14. <http://eudml.org/doc/221961>.

@article{Barcucci2010,

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.
},

author = {Barcucci, Elena, Brunetti, Sara, Ristoro, Francesco Del},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Polyomino; enumeration; succession rule; generating function
combinatorial
interpretation.; deco polyominoes; succession rules; Stirling numbers; Narayana and odd index Fibonacci numbers; generating functions},

language = {eng},

month = {3},

number = {1},

pages = {1-14},

publisher = {EDP Sciences},

title = { Succession rules and Deco polyominoes},

url = {http://eudml.org/doc/221961},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Barcucci, Elena

AU - Brunetti, Sara

AU - Ristoro, Francesco Del

TI - Succession rules and Deco polyominoes

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 1

SP - 1

EP - 14

AB -
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.

LA - eng

KW - Polyomino; enumeration; succession rule; generating function
combinatorial
interpretation.; deco polyominoes; succession rules; Stirling numbers; Narayana and odd index Fibonacci numbers; generating functions

UR - http://eudml.org/doc/221961

ER -

## References

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- M. Delest and X.G. Viennot, Algebraic languages and polyominoes enumeration. Theoret. Comput. Sci.34 (1984) 169-206. Zbl0985.68516
- R.L. Graham, D.E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley (1989).
- F.K. Hwang and C.L. Mallows, Enumerating Nested and Consecutive Partitions. J. Combin. TheorySer. A70 (1995) 323-333. Zbl0819.05005
- D.E. Knuth, The Art of Computer Programming, Vol. 1: Fundamental Algorithms. Addison Wesley, Reading Mass (1968). Zbl0191.17903
- G. Kreweras, Joint distributions of three descriptive parameters of bridges, edited by G. Labelle and P. Leroux, Combinatoire Énumérative, Montréal 1985. Springer, Berlin, Lecture Notes in Math.1234 (1986) 177-191.
- T.W. Narayana, Sur les treillis formés par les partitions d'un entier. C.R. Acad. Sci. Paris240 (1955) 1188-1189. Zbl0064.12705
- N.J.A. Sloane and S. Plouffe, The encyclopedia of integer sequences. Academic Press (1995). Zbl0845.11001

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