A functional equation arising from multiplication of quantum integers
Abstract
For the quantum integer [n]q = 1+q+...+qn-1 there is a natural polynomial multiplication *q such that [m]q *q [n]q = [mn]q. This multiplication leads to the functional equation fmn(q) = fm(q)fn(qm), defined on a given sequence (F)=\fn(q)\n=1∞ of polynomials. This paper contains various results concerning the classification and construction of polynomial sequences that satisfy the functional equation, as well as a list of open problems that arise fromthe classification.
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