유미수

Archive of posts with tag '유미수'

  • Meesue Yoo (유미수), Schur expansion of the integral form of Macdonald polynomials
    Schur expansion of the integral form of Macdonald polynomials
    Meesue Yoo (유미수)
    KIAS
    2013/10/30 Wednesday 4PM-5PM
    ROOM 1409
    In this talk, we consider the combinatorial formula for the Schur coefficients of the integral form of the Macdonald polynomials. As an attempt to prove Haglund’s conjecture that ⟨Jλ[X;q,qk]/(1-q)n,sμ(X)⟩∈ℕ[q], we have found explicit combinatorial formulas for the Schur coefficients in one row case, two column case and certain hook shape cases. Egge-Loehr-Warrington constructed a combinatorial way of getting Schur expansion of symmetric functions when the expansion of the function in terms of Gessel’s fundamental quasi symmetric functions is given. We apply this method to the combinatorial formula for the integral form Macdonlad polynomials of Haglund-Haiman-Loehr in quasi symmetric functions to get the Schur coefficients and prove the Haglund’s conjecture in more general cases.
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  • Meesue Yoo (유미수), p-rook numbers and cycle counting in the wreath product of Cp and Sn
    p-rook numbers and cycle counting in the wreath product of Cp and Sn
    Meesue Yoo (유미수)
    School of Mathematics, KIAS, Seoul, Korea
    2012/4/4 Wed 4PM-5PM
    The cycle counting rook numbers, hit numbers, and q-rook numberes and q-hit numbers have been studied by many people, and Briggs and Remmel introduced the theory of p-rook and p-hit numbers which is a rook theory model of the weath product of the cyclic group Cp and the symmetric group Sn.
    We extend the cycle-counting q-rook numberes and q-hit numbers to the Briggs-Remmel model. In such a settinig, we define multivariable version of the cycle-counting q-rook numbers and cycle-counting q-hit numbers where we keep track of cycles of pernutation and partial permutation of Cp wearth product with Sn according to the signs of the cycles.
    This work is a joint work with Jim Haglund at University of Pennsylvania and Jeff Remmel at UCSD.
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