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The expansion of Hall-Littlewood functions in the dual Grothendieck polynomial basis
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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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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     author = {Bandlow, Jason and Morse, Jennifer},
     title = {The expansion of {Hall-Littlewood} functions in the dual {Grothendieck} polynomial basis},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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Bandlow, Jason; Morse, Jennifer. The expansion of Hall-Littlewood functions in the dual Grothendieck polynomial basis. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2860. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2860/

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