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A Combinatorial Formula for the Schur Coefficients of the Integral Form of the Macdonald Polynomials in the Two Column and Certain Hook Cases

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Abstract

In this paper, we prove that the integral form of Macdonald polynomials J μ [X; q, t] has the property that J μ [X; q, t]/(1−q)n has Schur expansion with positive polynomial coefficient. Our proof proceeds by constructing constructing combinatorial formula for the Schur coefficients when μ is either a two column shape or a certain type of hook shape.

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  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Meesue Yoo

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  1. Meesue Yoo
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Correspondence to Meesue Yoo.

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Yoo, M. A Combinatorial Formula for the Schur Coefficients of the Integral Form of the Macdonald Polynomials in the Two Column and Certain Hook Cases. Ann. Comb. 16, 389–410 (2012). https://doi.org/10.1007/s00026-012-0133-x

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  • DOI: https://doi.org/10.1007/s00026-012-0133-x

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