Geodesic
A closed formula for the number of convex permutominoes
The electronic journal of combinatorics, Tome 14 (2007)

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In this paper we determine a closed formula for the number of convex permutominoes of size $n$. We reach this goal by providing a recursive generation of all convex permutominoes of size $n+1$ from the objects of size $n$, according to the ECO method, and then translating this construction into a system of functional equations satisfied by the generating function of convex permutominoes. As a consequence we easily obtain also the enumeration of some classes of convex polyominoes, including stack and directed convex permutominoes.
DOI : 10.37236/975
Classification : 05A15, 05B50
Mots-clés : number of convex permutominoes, recursive generation, Enumeration of Combinatorial Objects, ECO method 
Filippo Disanto; Andrea Frosini; Renzo Pinzani; Simone Rinaldi. A closed formula for the number of convex permutominoes. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/975
@article{10_37236_975,
     author = {Filippo Disanto and Andrea Frosini and Renzo Pinzani and Simone Rinaldi},
     title = {A closed formula for the number of convex permutominoes},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/975},
     zbl = {1158.05301},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/975/}
}
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