![]() N2 - We present an example of a quadratic algebra given by three generators and three relations, which is automaton (the set of normal words forms a regular language) and such that its ideal of relations does not possess a finite Gr\"obner basis with respect to any choice of generators and any choice of a well-ordering of monomials compatible with multiplication. Wisk.T1 - Quadratic automaton algebras and intermediate growth Wythoff, W.A.: A modification of the game of Nim. Smith, F., Stănică, P.: Comply/constrain games or games with a Muller twist. Larsson, U., Wästlund, J.: From heaps of matches to the limits of computability. MSRI Publications (Cambridge University Press) ![]() Larsson, U.: Restrictions of \(m\)-Wythoff Nim and \(p\)-complementary Beatty sequences. Larsson, U.: Impartial games emulating one-dimensional cellular automata and undecidability. Larsson, U.: 2-pile Nim with a restricted number of move-size imitations. MSRI Publications (Cambridge University Press), pp. Landman, H.A.: A simple FSM-based proof of the additive periodicity of the Sprague-Grundy function of Wythoff’s game. Holshouser, A., Reiter, H.: Three pile Nim with move blocking. The College Mathematics Journal 32(5), 382 (2001) ![]() Holshouser, A., Reiter, H.: Problems and solutions: Problem 714 (Blocking Nim). Hegarty, P., Larsson, U.: Permutations of the natural numbers with prescribed difference multisets. Gavel, H., Strimling, P.: Nim with a modular Muller twist. ![]() Gurvich, V.: Further generalizations of Wythoff’s game and minimum excludant function, RUTCOR Research Report, 16–2010, Rutgers University A 119(2), 450–459 (2012)įraenkel, A.S.: Complementing and exactly covering sequences. This process is experimental and the keywords may be updated as the learning algorithm improves.Ĭook, M., Larsson, U., Neary, T.: Generalized cyclic tag systems, with an application to the blocking queen game (in preparation)įink, A.: Lattice games without rational strategies. These keywords were added by machine and not by the authors. The patterns for large \(k\) display an unprecedented amount of self-organization at many scales, and here we attempt to describe the self-organized structure that appears. As \(k\) becomes large, parts of the pattern of winning positions converge to recurring chaotic patterns that are independent of \(k\). The value of \(k\) is a parameter that defines the game, and the pattern of winning positions can be very sensitive to \(k\). The game ends when a player wins by blocking all possible moves of the other player. The game, known as Blocking Wythoff Nim, consists of moving a queen as in chess, but always towards (0,0), and it may not be moved to any of \(k-1\) temporarily “blocked” positions specified on the previous turn by the other player. We show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton.
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