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Riordan group involutions. (English) Zbl 1131.05012

Summary: We study involutions in the Riordan group, especially those with combinatorial meaning. We give a new determinantal criterion for a matrix to be a Riordan involution and examine several classes of examples. A complete characterization of involutions in the Appell subgroup is developed. In another direction we find several examples that generalize the RNA matrix but are of independent interest.

MSC:

05A30 \(q\)-calculus and related topics
05A15 Exact enumeration problems, generating functions
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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