## Kevin Buchin, Man-Kwun Chiu, Stefan Felsner, Günter Rote, and
André Schulz:

# The number of convex polyominoes with given height and width

*manuscript, April 2019, 18 pages, arXiv:1903.01095 [math.CO],
* →BibTeX
### Abstract

We give a new combinatorial proof for the number of convex polyominoes whose
minimum enclosing rectangle has given dimensions. We also count the subclass
of these polyominoes that contain the lower left corner of the enclosing
rectangle (directed polyominoes). We indicate how to sample random polyominoes
in these classes. As a side result, we calculate the first and second
moments of the number of common points of two monotone lattice paths between
two given points.

Last update: March 5, 2019.