Sökning: "Beatty sequence"

Hittade 2 avhandlingar innehållade orden Beatty sequence.

1. 1. Sequences and games generalizing the combinatorial game of Wythoff Nim

   Författare :Urban Larsson; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Blocking manoeuvre; Beatty sequence; Combinatorial game; Complementary sequences; Impartial game; Interspersion array; Muller twist; Nim; Permutation of the natural numbers; Stolarsky array; Wythoff Nim; Beatty sequence;

   Sammanfattning : One single Queen is placed on an arbitrary starting position of a (large) Chess board. Two players alternate in moving the Queen as in a game of Chess but with the restriction that the $L^1$ distance to the lower left corner, position $(0,0)$, must decrease. The player who moves there wins. Let $\phi =\frac{1+\sqrt{5}}{2}$, the golden ratio. LÄS MER

3. 2. Impartial Games and Recursive Functions

   Författare :Urban Larsson; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Algorithmically undecidable; Beatty sequences; Blocking maneuver; Cellular automaton; Comply maneuver; Complementary sequences; Dictionary process; Dual game; Game complexity; Game convergence; Game reflexivity; Heap game; Impartial game; Invariant subtraction game; Move-size dynamic; Nim; P-equivalence; Rule 110; Splitting sequences; *-operator; Subtraction game; Take-away game; Turing complete; Wythoff Nim; Turing complete;

   Sammanfattning : Interest in 2-player impartial games often concerns the famous theory of Sprague-Grundy. In this thesis we study other aspects, bridging some gaps between combinatorial number theory, computer science and combinatorial games. LÄS MER