Wythoff Nim Extensions and Certain Beatty Sequences
Urban Larsson · 2008
The solution of Wythoff’s game—the set of P-positions— may be represented as a pair of sequences of non-negative integers, satisfying Beatty’s well-known theorem. We generalize the solution of Wythoff’s game to a pair of so-called m-complementary Beatty sequences. Our main result is that these sequences give the solution to three new extensions of Wythoff’s game—of which one has a certain blocking manoeuvre on the rook-type options.