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Is this matrix famous?

  1. Nov 10, 2008 #1
    Working in a counting complexity result, it came out this n x n matrix defined as follows:

    A_ij = comb(n+i-j,i) for each row i =1,...,n and each column j=1,...,n.

    NOTE: comb (a,b) represents a!/(b!(a-b)!) , which is the number of subsets of size b that can selected from a set of size a.

    I was wondering if anyone have seen this matrix before. I need to study the properties.

  2. jcsd
  3. Nov 12, 2008 #2
    nope, but just wondering what special properties does it have?
  4. Nov 12, 2008 #3
    This matrix appeared when i tried to prove that a counting problem was #p-complete using a polynomial interpolation technique. This matrix has full rank, and it's n-1 x n-1 upper right submatrix is equal to A(n-1).
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