Discrete Painlevé equations from different orthogonal polynomial weights share the D5(1) surface type but are inequivalent due to non-conjugate translations in the Weyl group and nodal curves, requiring a refined equivalence criterion that includes symmetry generators and parameter constraints.
MR3729446 [VAF03] Walter Van Assche and Mama Foupouagnigni,Analysis of non-linear recurrence relations for the re- currence coefficients of generalized Charlier polynomials, J
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On the discrete Painlev\'e equivalence problem, non-conjugate translations and nodal curves
Discrete Painlevé equations from different orthogonal polynomial weights share the D5(1) surface type but are inequivalent due to non-conjugate translations in the Weyl group and nodal curves, requiring a refined equivalence criterion that includes symmetry generators and parameter constraints.