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Multinomial convolution polynomials. (English) Zbl 0860.05005
The convolution polynomials $$F_{n_1,n_2,\dots,n_s}(x)$$ are defined as the coefficients of $$z^{n_1}_1z_2^{n_2}\cdots z^{n_s}_s$$ in
$$F(z_1,\dots,z_s)^x$$, where $$F(z_1,\dots,z_s)$$ is any formal power series with $$F(0,\dots,0)=1$$. The author studies multidimensional extensions of results of D. Knuth [Convolution polynomials, The Mathematical Journal 2, 67-78 (1992)]. Similar results have been obtained by J. Hofbauer [Beiträge zu Rota’s Theorie der Folgen von Binomialtyp, Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 187, 437-489 (1978; Zbl 0437.05004)].
Reviewer: J.Cigler (Wien)

##### MSC:
 05A19 Combinatorial identities, bijective combinatorics
##### Keywords:
convolution polynomials; coefficients; formal power series
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##### References:
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