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The expansion of Hall-Littlewood functions in the dual Grothendieck polynomial basis

Abstract : A combinatorial expansion of the Hall-Littlewood functions into the Schur basis of symmetric functions was first given by Lascoux and Schützenberger, with their discovery of the charge statistic. A combinatorial expansion of stable Grassmannian Grothendieck polynomials into monomials was first given by Buch, using set-valued tableaux. The dual basis of the stable Grothendieck polynomials was given a combinatorial expansion into monomials by Lam and Pylyavskyy using reverse plane partitions. We generalize charge to set-valued tableaux and use all of these combinatorial ideas to give a nice expansion of Hall-Littlewood polynomials into the dual Grothendieck basis. \par
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Jason Bandlow, Jennifer Morse. The expansion of Hall-Littlewood functions in the dual Grothendieck polynomial basis. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.145-154, ⟨10.46298/dmtcs.2860⟩. ⟨hal-01186288⟩

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