The University of Michigan Combinatorics Seminar
Schubert calculus studies questions of classical enumerative geometry. There are a number of ways to generalize Schubert calculus, and I'll define the class of generalizations named in the title.
In previous work with A.Buch and F.Sottile, it was explained why various questions arising from the theories of symmetric and Schubert polynomials are naturally special cases of this class of problems.
For these problems, we give a subtraction-free combinatorial rule for computing the answer. This covers cases previously studied by A.Buch and M.Kogan, and in particular generalizes the Littlewood-Richardson rule. There is also a Gröbner basis interpretation of this formula, one that geometrically explains the classical "transition" formula of Lascoux and Schützenberger.
This is joint work with A. Knutson.