Seminars in April 2012

  • Jack Koolen, On connectivity problems in distance-regular and strongly regular graphs
    On connectivity problems in distance-regular and strongly regular graphs
    Jack Koolen
    Department of Mathematics, POSTECH, Pohang, Korea
    2012/4/24 Tue 4PM-5PM
    In this talk I will discuss two problems of Andries Brouwer.
    In the first one he asked whether the minimal number of vertices you need to delete from a strongly regular graph with valency k and intersection numbers λ, μ, in order to disconnect it and such that each resulting component has at least two vertices is 2k-2-λ. We will show that there are strongly where you can use a smaller number of vertices to disconnect it in this way, but we also will give some positive results.
    The second question we discuss is how connected a distance-regular graph is far from a fixed vertex.
    This is joint work with Sebastian Cioaba and Kijung Kim.
    Tags:

  • 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.
    Tags:

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