Rectangular Polyomino Set Weak (1,2)-achievement Games

摘要

In a polyomino set (1,2)-achievement game the maker and the breakeralternately mark one and two previously unmarked cells respectively. Themaker's goal is to mark a set of cells congruent to one of a given set ofpolyominoes. The breaker tries to prevent the maker from achieving his goal.The teams of polyominoes for which the maker has a winning strategy isdetermined up to size 4. In set achievement games, it is natural to studyinfinitely large polyominoes. This enables the construction of super winnersthat characterize all winning teams up to a certain size.