Fun with polyominoes
by Douglas Rogers
Abstract:
A polyomino is a finite collection of cells in the square grid with connected interior – it is not enough that cells are connected only corner to corner, but a restriction on holes seem to be optional. The terminology was introduced (and later copyrighted) by Solomon Golomb, at a talk to the Harvard Mathematical Club in 1953. Instances had been considered earlier, since, after all, such cellular `animals’ are fairly natural creatures to consider, in play or as mathematical models. But Golomb was right to recognise the potential – even commercial possibilities – of polyominoes.
In this talk we take a look at some recent research. The talk draws in particular on two recent expository articles jointly with Simone Rinaldi that have appeared in The Mathematical Gazette:
- S. Rinaldi and D. G. Rogers: How the odd terms in the Fibonacci sequence stack up, 2007.
- S. Rinaldi and D. G. Rogers: Indecomposability: polyominoes and polyomino tilings, 2008.
- G. Castiglione et al.: Combinatorial aspects of L-convex polyominoes, European Journal of Combinatorics 28 (2007) pp1724–1741.