科研之友
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摘要
A subtraction game is an impartial combinatorial game involving a finite set S of positive integers. The nim-sequence G(S) associated with this game is ultimately periodic. In this paper, we study the nim-sequence G(S boolean OR{c}) where S is fixed and c varies. We conjecture that there is a multiple q of the period of G(S), such that for sufficiently large G(S boolean OR{c}), the pre-period and period of G(S boolean OR{c}) are linear in c if c modulo q is fixed. We prove it in several cases. @@@ We also give new examples with period 2 inspired by this conjecture.
