Niveau: Supérieur, Doctorat, Bac+8
Joint landscape on a peg solitaire board?† O. Ramaré, CNRS, Laboratoire Painlevé, Université Lille 1 59 655 Villeneuve d'Ascq, France May 31, 2011 Abstract We investigate and develop further the notions of joint landscape. 1 Introduction We introduced in (Ramaré, 2008c) the notion of landscape for a position I and in (Ramaré, 2008a) (see also the end of (Ramaré, 2008b)) the notion of joint landscape for two positions I and J . It is the function L(A, I, J) on S which is equal in A, when A /? I, to the minimal number of moves required to reach a position from which we may still derive J and which contains A, when starting from I. We have called this number the joint height h(A, I, J) of A with respect to be I and J , When A ? I, then ?L(A, I, J) is the minimal number of moves required to reach a position from which we may still derive J and which does not contain A. We call this number the joint depth of A with respect to I and J , an easy specialisation of the notion of depth introduced in section 11 of (Ramaré, 2008c). These heights, resp.
- whenever no
- final position
- solitaire board
- path verify
- height functions
- peg solitaire
- f1 ·
- external height
- lesser external height