A Monoid for the Universal K-Bruhat Order

Details A Monoid for the Universal K-Bruhat Order A Monoid for the Universal K-Bruhat Order

1997-12-17

arxiv.org/abs/math/9712258v1

European Journal of Combinatorics, 20, (1999), pp. 197-211.

Mathematics

Combinatorics

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

Scientific paper

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.

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