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In mathematics, a multiplicative sequence or ''m''-sequence is a sequence of polynomials associated with a formal group structure. They have application in the cobordism ring in algebraic topology. ==Definition== Let ''K''''n'' be polynomials over a ring ''A'' in indeterminates ''p''1,... weighted so that ''p''''i'' has weight ''i'' (with ''p''0 = 1) and all the terms in ''K''''n'' have weight ''n'' (so that ''K''''n'' is a polynomial in ''p''1, ..., ''p''''n''). The sequence ''K''''n'' is ''multiplicative'' if an identity : implies : The power series : is the ''characteristic power series'' of the ''K''''n''. 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''''j'' in the product : for any ''m'' > ''j''. This is symmetric in the ''β''''i'' and homogeneous of weight ''j'': so can be expressed as a polynomial ''K''''j''(''p''1, ..., ''p''''j'') in the elementary symmetric functions ''p'' of the ''β''. Then ''K''''j'' defines a multiplicative sequence. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「multiplicative sequence」の詳細全文を読む スポンサード リンク
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