Alain Lascoux

"Bruhat order, alternating sign matrices and Grothendieck polynomials"

The Ehresmann-Bruhat order on the symmetric group can be studied by embedding the symmetric group into the distributive lattice of alternating sign matrices. On the other hand, it is closely related to Schubert subvarieties of the flag manifold, and their classes in the Grothendieck ring ( Grothendieck polynomials). We show how to obtain Grothendieck polynomials as a simple statistics on alternating sign matrices.