Quasi-symmetric functions as polynomial functions on Young diagrams

Jean-Christophe Aval, Valentin Féray, Jean-Christophe Novelli, Jean-Yves Thibon

Published 2013-12-10, updated 2014-07-23Version 2

We determine the most general form of a smooth function on Young diagrams, that is, a polynomial in the interlacing or multirectangular coordinates whose value depends only on the shape of the diagram. We prove that the algebra of such functions is isomorphic to quasi-symmetric functions, and give a noncommutative analog of this result.