Multiplicative sequence: Difference between revisions

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==Definition==
Let ''K''<sub>''n''</sub> be polynomials over a ring ''A'' in indeterminates ''p''<sub>1</sub>,... weighted so that ''p''<sub>''i''</sub> has weight ''i'' (with ''p''<sub>0</sub> = 1) and all the terms in ''K''<sub>''n''</sub> have weight ''n'' (so that ''K''<sub>''n''</sub> is a polynomial in ''p''<sub>1</sub>,&nbsp;...,&nbsp;''p''<sub>''n''</sub>). The sequence ''K''<sub>''n''</sub> is ''multiplicative'' if an identity
 
:<math>\sum_i p_i z^i = \sum p'_i z^i \cdot \sum_i p''_i z^i </math>