김장수

Archive of posts with tag '김장수'

  • [Colloquium] Jang Soo Kim, Combinatorics of orthogonal polynomials
    Combinatorics of orthogonal polynomials
    Jang Soo Kim (김장수)
    Department of Mathematics, Sungkyunkwan University, Suwon
    2015/4/9 Thu 4:30PM-5:30PM (E6, Room 1501)
    Orthogonal polynomials are a family of polynomials which are orthogonal with respect to certain inner product. The n-th moment of orthogonal polynomials is an important quantity, which is given as an integral. In 1983 Viennot found a combinatorial expression for moments using lattice paths. In this talk we will compute the moments of several important orthogonal polynomials using Viennot’s theory. We will also see their connections with continued fractions, matchings, set partitions, and permutations.
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  • 2014 KAIST CMC Discrete Math Workshop
    2014 KAIST CMC Discrete Math Workshop
    December 10–12, 2014
    자연과학동(E6-1), KAIST

    Preregistration in kcw2014.eventbrite.com deadline: Dec. 5 (Friday)

    ABSTRACTS
    Program (Dec.10 Wed-Room 1409)
    • 1:30-2:00 Registration
    • 2:00-2:30 Young Soo Kwon (권영수), Yeungnam University: A variation of list coloring and its properties
    • 2:40-3:10 Mitsugu Hirasaka, Pusan National University: Small topics on association schemes
    • 3:10-3:40 Coffee Break
    • 3:40-4:10 Younjin Kim (김연진),  KAIST: On Extremal Combinatorial Problems of Noga Alon
    • 4:20-4:50 Jang Soo Kim (김장수),  Sungkyunkwan University: A new q-Selberg integral, Schur functions, and Young books
    • 5:00-6:00 Discussion
    • 6:00- Dinner
    Program (Dec.11 Thurs-Room 1501 & 3435)
    Program (Dec.12 Fri-Room 1501)
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  • Jang Soo Kim (김장수), Combinatorics of continued fractions and its application to Jacobi’s triple product identity
    Combinatorics of continued fractions and its application to Jacobi’s triple product identity
    Jang Soo Kim
    KIAS
    2013/09/25 Wed 4PM-5PM
    ROOM 1409
    In this talk we will see a combinatorial way to expand certain continued fractions using lattice paths called Motzkin paths. This method allows us to prove a formula for q-secant numbers. I will explain that this approach can be used to find a finite version of Jacobi’s triple product identity. This talk is based on my paper with Matthieu Josuat-Vergès: “Touchard-Riordan formulas, T-fractions, and Jacobi’s triple product identity”, The Ramanujan Journal, Volume 30, Issue 3, pp 341-378.
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  • Jang Soo Kim (김장수), Proofs of Two Conjectures of Kenyon and Wilson on Dyck Tilings
    Proofs of Two Conjectures of Kenyon and Wilson on Dyck Tilings
    Jang Soo Kim (김장수)
    School of Mathematics, University of Minnesota, Minneapolis, MN, USA
    2012/7/27 Fri 4PM-5PM
    Recently, Kenyon and Wilson introduced a certain matrix M in order to compute pairing probabilities of what they call the double-dimer model. They showed that the absolute value of each entry of the inverse matrix M-1 is equal to the number of certain Dyck tilings of a skew shape. They conjectured two formulas on the sum of the absolute values of the entries in a row or a column of M-1. In this talk we prove the two conjectures. As a consequence we obtain that the sum of the absolute values of all entries of M-1 is equal to the number of complete matchings. We also find a bijection between Dyck tilings and complete matchings.
    This talk is based on the following paper: arxiv:1108.5558.
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  • Jang Soo Kim (김장수), Combinatorics on permutation tableaux
    Combinatorics on permutation tableaux
    Jang Soo Kim (김장수)
    Laboratoire d’Informatique Algorithmique: Fondements et Applications (LIAFA), University of Paris 7, France
    2010/4/26 Mon 3PM-4PM (Room: 3433, Bldg E6-1)

    A permutation tableau is a relatively new combinatorial object introduced by Postnikov in his study of totally nonnegative Grassmanian. As one can guess from its name, permutation tableaux are in bijection with permutations. Surprisingly, there is also a connection between permutation tableaux and a statistical physics model called PASEP (partially asymmetric exclusion process). In this talk, we study some combinatorial properties of permutation tableaux. One of our result is a sign-imbalace formula for permutation tableaux which is very similar to the sign-imbalace formula for standard Young tableaux conjectured by Stanley.

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  • Jang Soo Kim (김장수), New Interpretations for Noncrossing Partitions of Classical Types
    New Interpretations for Noncrossing Partitions of Classical Types
    Jang Soo Kim (김장수)
    Laboratoire d’Informatique Algorithmique: Fondements et Applications (LIAFA), University of Paris 7, France
    2010/1/21 Thu 4PM-5PM

    The Catalan number \frac{1}{n+1}\binom{2n}{n} is perhaps the most frequently occurred number in combinatorics. Richard Stanley has collected more than 170 combinatorial objects counted by the Catalan number. Noncrossing partition, which has received great attention recently, is one of these, so called, Catalan objects. Noncrossing partitions are generalized to each finite Coxeter group. In this talk, we will interpret noncrossing partitions of type B in terms of noncrossing partitions of type A. As applications, we can prove interesting properties of noncrossing partitions of type B.

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  • Jang Soo Kim (김장수), A combinatorial approach to the power of 2 in the number of involutions
    A combinatorial approach to the power of 2 in the number of involutions
    Jang Soo Kim (김장수)
    Dept. of Mathematical Sciences, KAIST, Korea.
    2008/12/11 Thu, 5:30PM-6:30PM
    We prove combinatorially that the largest power of 2 in the number of involutions of length n is equal to [n/2]-2[n/4] +[(n+1)/4]. We show that the smallest period of the sequence of odd factors in the number of involutions modulo 2s is 2s+1 for s>2. We also consider the largest power of 2 in the number of even and odd involutions.
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