95 research outputs found
The number of directed k-convex polyominoes
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
Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice
Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate
the symmetry classes of convex hexagonal polyominoes. Here convexity is to be
understood as convexity along the three main column directions. We deduce the
generating series of free (i.e. up to reflection and rotation) and of
asymmetric convex hexagonal polyominoes, according to area and half-perimeter.
We give explicit formulas or implicit functional equations for the generating
series, which are convenient for computer algebra.Comment: 21 pages, 16 figures, 2 tables. This is the full version of a paper
presented at the FPSAC Conference in Vancouver, Canada, June 28 -- July 2,
200
A closed formula for the number of convex permutominoes
In this paper we determine a closed formula for the number of convex
permutominoes of size n. We reach this goal by providing a recursive generation
of all convex permutominoes of size n+1 from the objects of size n, according
to the ECO method, and then translating this construction into a system of
functional equations satisfied by the generating function of convex
permutominoes. As a consequence we easily obtain also the enumeration of some
classes of convex polyominoes, including stack and directed convex
permutominoes
- …