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- W2050003317 abstract "Given an operad P with a finite Gröbner basis of relations, we study the generating functions for the dimensions of its graded components P(n). Under moderate assumptions on the relations we prove that the exponential generating function for the sequence {dimP(n)} is differential algebraic, and in fact algebraic if P is a symmetrization of a non-symmetric operad. If, in addition, the growth of the dimensions of P(n) 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 {dimP(n)} is rational. We give a number of examples of calculations and discuss conjectures about the above generating functions for more general classes of operads." @default.
- W2050003317 created "2016-06-24" @default.
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- W2050003317 date "2015-03-01" @default.
- W2050003317 modified "2023-09-30" @default.
- W2050003317 title "On generating series of finitely presented operads" @default.
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- W2050003317 doi "https://doi.org/10.1016/j.jalgebra.2014.12.012" @default.
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