Variants of the RSK algorithm adapted to combinatorial Macdonald polynomials
نویسندگان
چکیده
منابع مشابه
A combinatorial model for the Macdonald polynomials.
We introduce a polynomial C(mu)[Z; q, t], depending on a set of variables Z = z(1), z(2),..., a partition mu, and two extra parameters q, t. The definition of C(mu) involves a pair of statistics (maj(sigma, mu), inv(sigma, mu)) on words sigma of positive integers, and the coefficients of the z(i) are manifestly in N[q,t]. We conjecture that C(mu)[Z; q, t] is none other than the modified Macdona...
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Abstract. In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of the formulas of Haglund-Haiman-Loehr for Macdonald polynoimals of type GLn. At q = 0 these formulas specialize to the formula of Schwer for the Macdonald spherical function in terms of positively folded alcove...
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The Macdonald polynomials H̃μ(x; q, t) have been the subject of much attention in combinatorics since Macdonald [25] defined them and conjectured that their expansion in terms of Schur polynomials should have positive coefficients. Macdonald’s conjecture was proven in [11] by geometric and representation-theoretic means, but these results do not provide any purely combinatorial interpretation fo...
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A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent-Littelmann and ...
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Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H(mu). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H(mu). As corollaries, we obtain the cocharge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization o...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2017
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2016.09.002