We give a new recursion formula for the number of convex polyominoes with fixed perimeter. From this we derive a bijection between an interval of natural numbers and the polyominoes of given perimeter. This provides a possibility to generate such polyominoes at random in polynomial time. Our method
Generating functions for column-convex polyominoes
β Scribed by M.P Delest
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 786 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0097-3165
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π SIMILAR VOLUMES
We give a 'beautiful' though complex -formula for the generating function Z of convex polyominoes, according to their area, width and height. Our method consists in solving a linear q-differential system of size three, which was derived two years ago by encoding convex polyominoes with the words of
We introduce a new class of plane figures: the sequences of tailed column-convex polyominoes (for short: stapoes). Let G(x, y) and l(x, y) denote the perimeter generating functions for columnconvex polyominoes and stapoes, respectively. It will be clear from the definitions that G(x, y) is a simple