A MONOID FOR THE UNIVERSAL k-BRUHAT ORDER
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چکیده
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∞, the universal k-Bruhat order. Here we present a monoid M for this order. We show that M is analogous to the nil-Coxeter monoid for the weak order on S∞. For this, we develop the theory of reduced sequences for M. We use these sequences to give a combinatorial description of the structure constants above. We also give a combinatorial proof of some of the symmetry relations satisfied by these constants.
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تاریخ انتشار 1997