A positive combinatorial formula for symplectic Kostka–Foulkes polynomials I: Rows
نویسندگان
چکیده
منابع مشابه
A Combinatorial Formula for Macdonald Polynomials
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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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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The Jack polynomials Jλ(x; α) form a remarkable class of symmetric polynomials. They are indexed by a partition λ and depend on a parameter α. One of their properties is that several classical families of symmetric functions can be obtained by specializing α, e.g., the monomial symmetric functions mλ (α = ∞), the elementary functions eλ′ (α = 0), the Schur functions sλ (α = 1) and finally the t...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2020.05.030