  The generalized Kostka polynomials are the Poincare polynomials of isotypic
components of certain graded GL(n)-modules. The former satisfy a monotonicity
property arising from natural surjections of the corresponding modules. This
monotonicity property is realized combinatorially by a directed system of
order- and statistic-preserving embeddings between the sets of
Littlewood-Richardson (LR) tableaux that describe the generalized Kostka
polynomials. Each set of LR tableaux is embedded into a cocyclage poset of
column-strict tableaux of a fixed content, and the image is characterized in
terms of catabolizable tableaux.
