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 On generating series of finitely presented operads


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Given an operad P with a finite Gr\-obner basis of relations, we study the generating functions for the dimensions of its graded components Pn. Under moderate assumptions on the relations we prove that the exponential generating function for the sequence {dim Pn} is differential algebraic, and in fact algebraic for P is a symmetrization of a non-symmetric operad. If, in addition, the growth of the dimensions Pn is bounded by an exponent of n or a polynomial of n, in the non-symmetric case then, Moreover, the ordinary generating function for the above sequence {dim Pn} is rational. We give a number of examples of calculations and discuss conjectures about the above generating functions for more general classes of operads.



Autor: Anton Khoroshkin; Dmitri Piontkovski

Fuente: https://archive.org/



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