ON SOME SYMPLECTIC GROUP ACTIONS WHERE ALL THE ORBITS ARE EQUIVARIANTLY ISOMORPHIC AND DIFFEOMORPHIC TO A FIXED ORBIT OF THE COADJOINT ACTION

In conformity with the 'Foundations of Mechanics' given by R. ABRAHAM and J. E. MARSDEN [1] let (P,w) be a symplectic manifold and Φ:GxP-P a Hamiltonian action of a compact, connected Lie group G on the manifold P. Considering this setting J. SZENTHE [2] found the following result: If the isotropy subgroups of the action Φ are of maximal rank then all the orbits of Φ are equivariantly isomorphic. Consequently, P is the total space of a differentiable fibre bundle, where the base manifold is the orbit space of the action Φ and the fibres are diffeomorphic to a fixed orbit of the coadjoint action. The aim of the present paper is to develop further characterizations of the above situation as it was suggested by J. J. DUISTERMAAT

On three-rowed Chomp

Chomp is a 50 year-old game played on a partially ordered set P. It has been in the center of interest of several mathematicians since then. Even when P is simply a 3 × n lattice, we have almost no information about the winning strategy. In this paper we present a new approach and a cubic algorithm for computing the winning positions for this case. We also prove that from the initial positions there are infinitely many winning moves in the third row