arXiv subjects

Samin Ingrith Ceron

Publications and source records attributed to Samin Ingrith Ceron.

2 recordsLinked to original sources

arXiv2026

Matrix representations and arithmetic properties of jacobsthal numbers via binary 3x3 matrices

We study matrix representations of the Jacobsthal sequence generated by binary 3x3 matrices with determinants 0, 2, and -2, using linear algebraic methods analogous to Fibonacci-type constructions. Explicit formulas for matrix powers are obtained, yielding identities for Jacobsthal numbers, including convolution formulas, trace relations, determinant expressions, and Cassini-type identities. We further derive congruence relations and recurrence formulas, and analyze arithmetic properties such as partial sums and the Sidon-type structure of the sequence. Finally, we prove that exactly three conjugacy classes of binary 3x3 matrices generate the Jacobsthal sequence, providing a unified algebraic framework that connects matrix theory with second-order linear recurrences.

math.NT↗

arXiv2024

Construction of some non-associative algebras from Associative Algebras with an endomorphism operator, a differential operator or a left averaging operator

In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a skew-idempotent or an idempotent element. These maps on associative algebra induce a non-associative algebra structure such as Lie algebra, Pre-Lie algebra, Jordan algebra, Flexible Algebra or (left) Leibniz algebra. We consider the construction of non-associative algebras from associative algebras with Linear Operators as the main results of this work. In this paper we give examples of non-associative algebras on subspaces of square matrices M3(R).

math.RA↗