This chapter concerns edge labeled Young tableaux, introduced by H. Thomas
and the third author. It is used to model equivariant Schubert calculus of
Grassmannians. We survey results, problems, conjectures, together with their
influences from combinatorics, algebraic and symplectic geometry, linear
algebra, and computational complexity. We report on a new shifted analogue of
edge labeled tableaux. Conjecturally, this gives a Littlewood-Richardson rule
for the structure constants of the D. Anderson-W. Fulton ring, which is related
to the equivariant cohomology of isotropic Grassmannians.Comment: 39 page