In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials

assess their own thought processes in an internal dialogue similar to reasoned debate among group members; and to represent features of the world, not just as your perspective or my perspective, but as objectively true, as facts. Evolutionary psychology is a crowded market. There’s no shortage of books telling a story about how chimp-like ancestors turned into modern humans. A Natural History o...

A power series is introduced that is an extension to three sets of variables of the Cauchy sum for Jack symmetric functions in the Jack parameter : We conjecture that the coeecients of this series with respect to the power sum basis are nonneg-ative integer polynomials in b, the Jack parameter shifted by 1. More strongly, we make the Matchings-Jack Conjecture, that the coeecients are counting s...