Abstract
The quantum integer [n]q is the polynomial 1 + q + q2 + ⋯ + qn-1, and the sequence of polynomials [Formula: see text] is a solution of the functional equation fmn(q) = fm(q)fn(qm). In this paper, semidirect products of semigroups are used to produce families of functional equations that generalize the functional equation for quantum multiplication.
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