Grothendieck polynomials via permutation patterns and chains in the Bruhat order

Details Grothendieck polynomials via permutation patterns and chains in the Bruhat order Grothendieck polynomials via permutation patterns and chains in the Bruhat order

2004-05-28

arxiv.org/abs/math/0405539v2

American Journal of Mathematics, 128, No. 4, (2006), 805--848.

Mathematics

Combinatorics

35 pages. Revised from the original

Scientific paper

We give new formulas for Grothendieck polynomials of two types. One type expresses any specialization of a Grothendieck polynomial in at least two sets of variables as a linear combination of products Grothendieck polynomials in each set of variables, with coefficients Schubert structure constants for Grothendieck polynomials. The other type is in terms of chains in the Bruhat order. We compare this second type to other constructions of Grothendieck polynomials within the more general context of double Grothendieck polynomials and the closely related H-polynomials. Our methods are based upon the geometry of permutation patterns.

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