A Monoid for the Universal K-Bruhat Order

Abstract

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.

LaTeX-2e, 21 pages, 3 figures, uses epsf.sty

References in corpus (3)

• Schubert polynomials, the Bruhat order, and the geometry of flag manifolds
• A Pieri-type formula for isotropic flag manifolds
• Universal Schubert polynomials

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• Positroid varieties I: juggling and geometry
• A Pieri-type formula for isotropic flag manifolds
• A special case of sl(n)-fusion coefficients
• Fomin-Greene monoids and Pieri operations
• A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
• A Pieri-type formula for the K-theory of a flag manifold
• A quantum Murnaghan--Nakayama rule for the flag manifold