13,476 research outputs found
Biased Weak Polyform Achievement Games
In a biased weak polyform achievement game, the maker and the breaker
alternately mark previously unmarked cells on an infinite board,
respectively. The maker's goal is to mark a set of cells congruent to a
polyform. The breaker tries to prevent the maker from achieving this goal. A
winning maker strategy for the game can be built from winning
strategies for games involving fewer marks for the maker and the breaker. A new
type of breaker strategy called the priority strategy is introduced. The
winners are determined for all pairs for polyiamonds and polyominoes up
to size four
On the Hausdorff dimension of the Rauzy gasket
In this paper, we prove that the Hausdorff dimension of the Rauzy gasket is
less than 2. By this result, we answer a question addressed by Pierre Arnoux.
Also, this question is a very particular case of the conjecture stated by S.P.
Novikov and A. Ya. Maltsev in 2003.Comment: 23 pages, 5 figure
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