On generating series of finitely presented operads

Autor:	Khoroshkin, Anton, Piontkovski, Dmitri
Rok vydání:	2012
Předmět:	Mathematics - Quantum Algebra Mathematics - Algebraic Topology Mathematics - Combinatorics Mathematics - Rings and Algebras 18D50 16S15 05E15 05A15
Zdroj:	Journal of Algebra (2015), pp. 377-429
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jalgebra.2014.12.012
Popis:	Given an operad P with a finite Groebner 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 {dim P(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 {dim P(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. Comment: Minor changes; references to recent articles by Berele and by Belov, Bokut, Rowen, and Yu are added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1202.5170 Zobrazit plný text záznamu View this record from Arxiv