Corpus ID: 2833587

The number of $k$-parallelogram polyominoes

@article{Battaglino2013TheNO,
title={The number of \$k\$-parallelogram polyominoes},
author={Daniela Battaglino and J. Fedou and S. Rinaldi and S. Socci},
journal={Discrete Mathematics \& Theoretical Computer Science},
year={2013},
pages={1113-1124}
}
A convex polyomino is $k$-$\textit{convex}$ if every pair of its cells can be connected by means of a $\textit{monotone path}$, internal to the polyomino, and having at most $k$ changes of direction. The number $k$-convex polyominoes of given semi-perimeter has been determined only for small values of $k$, precisely $k=1,2$. In this paper we consider the problem of enumerating a subclass of $k$-convex polyominoes, precisely the $k$-$\textit{convex parallelogram polyominoes}$ (briefly, \$k… Expand
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