Geodesic
Staircase Macdonald polynomials and the $q$-Discriminant
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008).

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We prove that a $q$-deformation $\mathfrak{D}_k(\mathbb{X};q)$ of the powers of the discriminant is equal, up to a normalization, to a specialization of a Macdonald polynomial indexed by a staircase partition. We investigate the expansion of $\mathfrak{D}_k(\mathbb{X};q)$ on different bases of symmetric functions. In particular, we show that its expansion on the monomial basis can be explicitly described in terms of standard tableaux and we generalize a result of King-Toumazet-Wybourne about the expansion of the $q$-discriminant on the Schur basis. 
@article{DMTCS_2008_special_255_a9,
     author = {Boussicault, Adrien and Luque, Jean-Gabriel},
     title = {Staircase {Macdonald} polynomials and the $q${-Discriminant}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     year = {2008},
     doi = {10.46298/dmtcs.3601},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3601/}
}
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%A Luque, Jean-Gabriel
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%J Discrete mathematics & theoretical computer science
%D 2008
%V DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
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Boussicault, Adrien; Luque, Jean-Gabriel. Staircase Macdonald polynomials and the $q$-Discriminant. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi : 10.46298/dmtcs.3601. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3601/

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