%0 Journal Article
%T A Monoid for the Universal K-Bruhat Order
%A Nantel Bergeron
%A Frank Sottile
%J Mathematics
%D 1997
%I arXiv
%X Structure constants for the multiplication of Schubert polynomials by Schur symmetric polynomials are known to be related to the enumeration of chains in a new partial order on S_\infty, which we call the universal k-Bruhat order. Here we present a monoid M for this order and show that $M$ is analogous to the nil-Coxeter monoid for the weak order on S_\infty. For this, we develop a theory of reduced sequences for M. We use these sequences to give a combinatorial description of the structure constants above. We also give combinatorial proofs of some of the symmetry relations satisfied by these structure constants.
%U http://arxiv.org/abs/math/9712258v1