Some notes on the algebraic structure of linear recurrent sequences
Number Theory
2023-02-28 v1
Abstract
Several 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 are R-algebras, given any commutative ring 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 algebras are isomorphic, considering also the R-algebras obtained using the Hadamard product and the convolution product.
Cite
@article{arxiv.2302.13867,
title = {Some notes on the algebraic structure of linear recurrent sequences},
author = {Gessica Alecci and Stefano Barbero and Nadir Murru},
journal= {arXiv preprint arXiv:2302.13867},
year = {2023}
}