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Schubert polynomial expansions revisited
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abstract
We give an elementary approach utilizing only the divided difference formalism for obtaining expansions of Schubert polynomials that are manifestly nonnegative, by studying solutions to the equation $\sum Y_i\partial_i=\mathrm{id}$ on polynomials with no constant term. This in particular recovers the pipe dream and slide polynomial expansions. We also show that slide polynomials satisfy an analogue of the divided difference formalisms for Schubert polynomials and forest polynomials, which gives a simple method for extracting the coefficients of slide polynomials in the slide polynomial decomposition of an arbitrary polynomial.
Forward citations
Cited by 2 Pith papers
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Cauchy identities for Grothendieck polynomials and a dual RSK correspondence through pipe dreams
A new algorithm, pipe dream rectification, bijectively realizes the Cauchy identities for Grothendieck polynomials and leads to a pipe-dream version of dual RSK insertion.
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Equivariant quasisymmetry and noncrossing partitions
A new equivariant version of quasisymmetric polynomials is introduced, giving double forest polynomials with noncrossing-partition evaluation formulas, Graham-positive structure constants, and a Bruhat-order character...
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