Back
 OJDM  Vol.9 No.2 , April 2019
2-Convex Polyominoes: Non-Empty Corners
Abstract: A polyomino P is called 2-convex if for every two cells there exists a monotone path included in P with at most two changes of direction. This paper studies the geometrical properties of a sub-class of 2-convex polyominoes called where the upper left corner and the lower right corner of the polyomino each contains only one cell.
Cite this paper: Tawbe, K. , Ghandour, N. and Atwi, A. (2019) 2-Convex Polyominoes: Non-Empty Corners. Open Journal of Discrete Mathematics, 9, 33-51. doi: 10.4236/ojdm.2019.92005.
References

[1]   Barcucci, E., Del Lungo, A., Nivat, M. and Pinzani, R. (1996) Reconstructing Convex Polyominoes from Horizontal and Vertical Projections. Theoretical Computer Science, 155, 321-347.
https://doi.org/10.1016/0304-3975(94)00293-2

[2]   Brunetti, S. and Daurat, A. (2005) Random Generation of Q-Convex Sets. Theoretical Computer Science, 347, 393-414.
https://doi.org/10.1016/j.tcs.2005.06.033

[3]   Castiglione, G., Restivo, A. and Vaglica, R. (2006) A Reconstruction Algorithm for L-Convex Polyominoes. Theoretical Computer Science, 356, 58-72.
https://doi.org/10.1016/j.tcs.2006.01.045

[4]   Tawbe, K. and Vuillon, L. (2011) 2L-Convex Polyominoes: Geometrical Aspects. Contributions to Discrete Mathematics, 6, 1-25.

[5]   Tawbe, K. and Vuillon, L. (2013) 2L-Convex Polyominoes: Tomographical Aspects. Contributions to Discrete Mathematics, 8, 1-12.

[6]   Castiglione, G., Frosini, A., Munarini, E., Restivo, A. and Rinaldi, S. (2007) Combinatorial Aspects of L-Convex Polyominoes. European Journal of Combinatorics, 28, 1724-1741.
https://doi.org/10.1016/j.ejc.2006.06.020

[7]   Castiglione, G. and Restivo, A. (2003) Reconstruction of L-Convex Polyominoes. Electronic Notes in Discrete Mathematics, 12.

[8]   Chrobak, M. and Dürr, C. (1999) Reconstructing hv-Convex Polyominoes from Orthogonal Projections. Information Processing Letters, 69, 283-289.
https://doi.org/10.1016/S0020-0190(99)00025-3

 
 
Top