Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant properties for Wronskian type determinants of classical and
  classical discrete orthogonal polynomials under an involution of sets of
  positive integers   Given a finite set $F=\{f_1,\cdots ,f_k\}$ of nonnegative integers (written
in increasing size) and a classical discrete family $(p_n)_n$ of orthogonal
polynomials (Charlier, Meixner, Krawtchouk or Hahn), we consider the Casorati
determinant $\det(p_{f_i}(x+j-1))_{i,j=1,\cdots,k}$. In this paper we prove a
nice invariant property for this kind of Casorati determinants when the set $F$
is changed by $I(F)=\{0,1,2,\cdots,\max F\}\setminus \{\max F-f:f\in F\}$. This
symmetry is related to the existence of higher order difference equations for
the orthogonal polynomials with respect to certain Christoffel transforms of
the classical discrete measures. By passing to the limit, this invariant
property is extended for Wronskian type determinants whose entries are Hermite,
Laguerre and Jacobi polynomials.

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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat