Row-convex tableaux and the combinatorics of initial terms
A row-convex shape is a generalization of a Young diagram in which the only restriction is a shape which has no gaps in any row. A straight tableau is similar to a standard tableau whose column strict condition has been relaxed in a specific way. Via an algorithmic content preserving bisection between straight and standard tableaux and the inverse of the bisection we obtain a basis for the Schur module associated with a row-convex shape. The initial terms under a diagonal term order are also described, and the set of biwords corresponding to these terms is shown to be dual-Knuth closed. A corollary to a theorem on sorted biwords and straight tableaux yields that the recording tableaux for biwords corresponding to initial terms are decomposable. To conclude the matrix for the natural action of bases for the Schur module associated with a row-convex shape is shown to be unitriangular.
scientific article; zbMATH DE number 1453363