We present an algorithm for finding a system of recurrence relations for the number of permutations of length n that satisfy a certain set of conditions. A rewriting of these relations automatically gives a system of functional equations satisfied by the multivariate generating function that counts permutations by their length and the indices of the corresponding recurrence relations. We propos...

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Abstract The main difference between certain spectral problems for linear Schrödinger operators, e.g. the almost Mathieu equation, and three-term recurrence relations for orthogonal polynomials is that in the former the index ranges across Z and in the latter only across Z+. We present a technique that, by a mixture of Dirichlet and Taylor expansions, translates the almost Mathieu equation and ...

In this paper, monic polynomials orthogonal with deformation of the Freud-type weight function are considered. These fullfill linear differential equation some polynomial coefficients in their holonomic form. The aim work is explore certain characterizing properties perturbed Freud type such as nonlinear recursion relations, finite moments, differential-recurrence and relations satisfied by rec...