Sobolev orthogonal polynomials in computing of Hankel determinants (Q1758446)

The closed form computation of Hankel determinants is of great combinatorial interest related to partitions and permutations. In this paper, the authors study closed form evaluation of some special Hankel determinants. They show that such problems are directly connected with the theory of quasi-definite discrete Sobolev orthogonal polynomials by considering a discrete Sobolev inner product, that is, an ordinary inner product plus an atomic inner product. Although a lot of methods are previously known for computation of Hankel determinants, the usage of Sobolev orthogonal polynomials is quite new.