Geodesic
The number of directed $k$-convex polyominoes
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/row and number of corners. This method can be used to study different families of directed convex polyominoes: symmetric polyominoes, parallelogram polyominoes. In this paper, we apply our method to determine the generating function for directed $k$-convex polyominoes.We show it is a rational function and we study its asymptotic behavior. 
@article{DMTCS_2015_special_285_a9,
     author = {Boussicault, Adrien and Rinaldi, Simone and Socci, Samanta},
     title = {The number of directed $k$-convex polyominoes},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2465},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2465/}
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Boussicault, Adrien; Rinaldi, Simone; Socci, Samanta. The number of directed $k$-convex polyominoes. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2465. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2465/

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