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In [[mathematics]], a '''multiplicative sequence''' or '''''m''-sequence''' is a sequence of [[polynomial]]s associated with a formal [[group theory|group]] structure. They have application in the [[cobordism|cobordism ring]] in [[algebraic topology]].
==Definition==
Let ''K''<sub>''n''</sub> be polynomials over a [[ring (mathematics)|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>, ..., ''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>
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:<math>\sum K_n(1,0,\ldots,0) z^n </math>
is the ''characteristic power series'' of the ''K''<sub>''n''</sub>. A multiplicative sequence is determined by its characteristic power series ''Q''(''z''), and every [[power series]] with constant term 1 gives rise to a multiplicative sequence.
To recover a multiplicative sequence from a characteristic power series ''Q''(''z'') we consider the coefficient of ''z''<sup>''j''</sup> in the product
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