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Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version) (0807.1523v2)
Published 9 Jul 2008 in cs.DM and math.CO
Abstract: The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Ces`aro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence; the coefficients are obtained through some dilation equations. The proofs are based on elementary linear algebra.