A method for the enumeration of various classes of column-convex polygons
Discrete Mathematics
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Reconstruction of convex 2D discrete sets in polynomial time
Theoretical Computer Science
On Piecewise Testable, Starfree, and Recognizable Picture Languages
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
On well quasi-orders on languages
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Theoretical Computer Science - The art of theory
Enumeration of L-convex polyominoes by rows and columns
Theoretical Computer Science
A reconstruction algorithm for L-convex polyominoes
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Combinatorial aspects of L-convex polyominoes
European Journal of Combinatorics
Recognizable picture languages and polyominoes
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
A tiling system for the class of L-convex polyominoes
Theoretical Computer Science
Hi-index | 0.00 |
We introduce a partial order on pictures (matrices), denoted by ≼ that extends to two dimensions the subword ordering on words. We investigate properties of special families of discrete sets (corresponding to {0,1}-matrices) with respect to this partial order. In particular we consider the families of polyominoes and convex polyominoes and the family, recently introduced by the authors, of L-convex polyominoes. In the first part of the paper we study the closure properties of such families with respect to the order. In particular we obtain a new characterization of L-convex polyominoes: a discrete set P is a L-convex polyomino if and only if all the elements Q≼P are polyominoes. In the second part of the paper we investigate whether the partial orderings introduced are well-orderings. Since our order extends the subword ordering, which is a well-ordering (Higman's theorem), the problem is whether there exists some extension of Higman's theorem to two dimensions. A negative answer is given in the general case, and also if we restrict ourselves to polyominoes and even to convex polyominoes. However we prove that the restriction to the family of L-convex polyominoes is a well-ordering. This is a further result that shows the interest of the notion of L-convex polyomino.