4 citations · 4 across the 3 of their papers we have counts for
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Invariant number triangles, eigentriangles and Somos-4 sequences
Paul Barry
Using the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, th…
Combinatorial polynomials as moments, Hankel transforms and exponential Riordan arrays
Paul Barry
In the case of two combinatorial polynomials, we show that they can exhibited as moments of paramaterized families of orthogonal polynomials, and hence derive their Hankel transfor…
Eulerian polynomials as moments, via exponential Riordan arrays
Paul Barry
Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, are mom…
An orthogonal polynomial coefficient formula for the Hankel transform
Paul Barry
We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply t…
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms
Paul Barry
Taking the examples of Legendre and Hermite orthogonal polynomials, we show how to interpret the fact that these orthogonal polynomials are moments of other orthogonal polynomials…
Riordan arrays and the LDU decomposition of symmetric Toeplitz plus Hankel matrices
Paul Barry, Aoife Hennessy
We examine a result of Basor and Ehrhardt concerning Hankel and Toeplitz plus Hankel matrices, within the context of the Riordan group of lower-triangular matrices. This allows us…