Enumeration of L-convex polyominoes by rows and columns

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once. Using the ECO method, we prove that the number f n of L-...

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Vydáno v:Theoretical computer science Ročník 347; číslo 1; s. 336 - 352
Hlavní autoři: Castiglione, G., Frosini, A., Restivo, A., Rinaldi, S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 30.11.2005
Elsevier
Témata:
Applied sciences
Computer science; control theory; systems
Convex polyominoes
Difference and functional equations, recurrence relations
ECO method
Exact sciences and technology
Generating functions
Mathematics
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Theoretical computing
Convex polyominoes
ECO method
Generating functions
Recurrence
Generating functions: ECO method
Enumeration
Generating function
Computer theory
Column
Recurrence relation
Columns
Interpretation
Cell
Direction
ISSN:0304-3975, 1879-2294
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Popis
Shrnutí:In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once. Using the ECO method, we prove that the number f n of L-convex polyominoes with perimeter 2 ( n + 2 ) satisfies the rational recurrence relation f n = 4 f n - 1 - 2 f n - 2 , with f 0 = 1 , f 1 = 2 , f 2 = 7 . Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2005.06.031