Exhaustive generation of gominoes
Theoretical Computer Science
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An n-omino is a plane figure composed of n unit squares joined together along their edges. Every n-omino is generated by joining the edge of a unit square to the edge of a unit square in some (n-1)-omino so that the new square does not overlap any squares. Let t(n) denote the number of n-ominoes, then it is known that the sequence ${((t(n))}^{1/n} : n = 1,2,\ldots )$ increases to a limit $\Theta$ , and 3.72 $\Theta$ 6.75 . A procedure exists for computing an increasing sequence of numbers bounded above by $\Theta$. (Chandra recently showed that the limit of this sequence is $\Theta$ .) In the present work we give a procedure for computing a sequence of numbers bounded below by $\Theta$ . Whether or not the limit of this sequence is $\Theta$ remains an open question. By computing the first ten terms of our sequence, we have shown that $\Theta$ 4.65 .