Author:
Alecci Gessica,Barbero Stefano,Murru Nadir
Abstract
AbstractSeveral operations can be defined on the set of all linear recurrent sequences, such as the binomial convolution (Hurwitz product) or the multinomial convolution (Newton product). Using elementary techniques, we prove that this set equipped with the termwise sum and the aforementioned products is an R-algebra, given any commutative ring R with identity. Moreover, we provide explicitly a characteristic polynomial of the Hurwitz product and Newton product of any two linear recurrent sequences. Finally, we also investigate whether these R-algebras are isomorphic, considering also the R-algebras obtained using the Hadamard product and the convolution product.
Funder
Università degli Studi di Trento
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics
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