Minimum sets of partial polyominoes

problems about polyominoes have been discussed. \Ve introduce new one: Determine the smallest size fen) of cut-set C(n) of n-ominoes, such that every sufficiently polyomino contains at one n-omino C(n) a partial polyomino. This question may be of interest in biology or pharmacy, for ex:arrlpl IC, if every infinite cell of polyominoes can be avoided the control of all nominoes for fixed n then it would suffice to control those of C(n). A minimum cut-set C(n) will be denoted by T(n). A first observation is that snakes have to be considered. A snake is polyomino "I",here two squares, the endsquares, have a side in common with one, and all other squares have two sides in common with two of the other squares of the polyomino. Any growing polyomino contains also grO\ving snakes. So we have to look for a minimum cut-set T( n), so that every infinite snake contains at least one n-snake of as a partial polyomino. The first numbers s( n) of different snakes with n squares