A q-Polynomial Identity
Copyright policy )A q-Polynomial Identity
This q-polynomial identity involves the number of inversions between multisets \((a_ 1,...,a_ n)\) and \((m-a_ 1,...,m-a_ n)\), and generalizes the recurrence identity for q-binomial (Gaussian) coefficients [\textit{I. P. Goulden} and \textit{D. M. Jackson}, Combinatorial enumeration (1983; Zbl 0519.05001), p. 100] and the polynomial coefficient recurrence [\textit{L. Comtet}, Advanced combinatorics (1974; Zbl 0283.05001), p. 77].
polynomial coefficient recurrence, q-polynomial identity, Arithmetic functions; related numbers; inversion formulas, recurrence identity, Combinatorial identities, bijective combinatorics, q-binomial coefficients
polynomial coefficient recurrence, q-polynomial identity, Arithmetic functions; related numbers; inversion formulas, recurrence identity, Combinatorial identities, bijective combinatorics, q-binomial coefficients
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