 
Summary: On the binary solitaire cone
David Avis a,1 Antoine Deza b,c,2
a McGill University, School of Computer Science, Montr’eal, Canada
b Tokyo Institute of Technology, Department of Mathematical and Computing
Sciences. Tokyo, Japan
c Ecole des Hautes Etudes en Sciences Sociales, Centre d'Analyse et de
Math’ematique Sociales, Paris, France
Abstract
The solitaire cone SB is the cone of all feasible fractional Solitaire Peg games.
Valid inequalities over this cone, known as pagoda functions, were used to show the
infeasibility of various peg games. The link with the well studied dual metric cone
and the similarities between their combinatorial structures see (3) leads to the
study of a dual cut cone analogue; that is, the cone generated by the {0, 1}valued
facets of the solitaire cone. This cone is called binary solitaire cone and denoted
BSB . We give some results and conjectures on the combinatorial and geometric
properties of the binary solitaire cone. In particular we prove that the extreme rays
of SB are extreme rays of BSB strengthening the analogy with the dual metric cone
whose extreme rays are extreme rays of the dual cut cone. Other related cones are
also considered.
1 Introduction and Basic Properties
