Anti-ribbon shaped Young diagram decomposition

Abstract

We introduce a sliding procedure on diagrams which splits the standard Young tableaux of a corner-crossed diagram, in particular of a skew shape, along a finite binary tree whose leaves are anti-ribbon diagrams. Combined with standardization, this yields a decomposition of semi-standard Young tableaux into tableaux of anti-ribbon shape, indexed by standard tableaux and governed by their descent sets. As applications, we obtain expansions of Schur functions and Schur multiple zeta functions in terms of their anti-ribbon type analogues; at the level of Schur functions, this is a tableau-level form of Gessel's fundamental quasisymmetric expansion.