Abstract

We introduce and study a combinatorial invariant associated with row-strict tableaux of a fixed partition shape   For a tableau T, we de ne an invariant vector  obtained from the incremental structure of the tableau and consider the associated weight statistic.

This statistic gives rise to a generating polynomial

Which encodes the distribution of the invariant over all row-strict tableaux of shape λ.

We investigate structural properties of this invariant and analyze the behavior of the generating polynomial through explicit enumeration for small partitions. In particular, we obtain formulas for the invariant in the case of strictly decreasing partitions and identify basic bounds for the weight statistic. Computational data suggest interesting symmetry pat- terns in the generating polynomials, including instances of palindromicity for certain partition shapes.

These results provide a combinatorial framework for studying row- strict tableaux through generating functions and suggest possible connections with permutation statistics and combinatorial structures arising in the study of Springer varieties.

Keywords

Springer varieties; Row-strict tableaux; Schubert varieties; Tymoczko codes; Generating functions; Betti numbers

Introduction