Recurrence relations over division algebras

2025/09/22 by Adam Chapman, Chapman, Adam, Solomon Vishkautsan +1
Computer Science · #11B37 #12E15 #15A18 #15B33 #16K20 #17A35 #17A75 #Advanced Algebra and Logic #FOS: Mathematics #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2509.17826

openalex publication_date 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials to the non-commutative setting. We then solve linear recurrences of order 2 over octonion division algebras.

Citations

• Roots and Critical Points of Polynomials over Cayley--Dickson Algebras
• Factoring Octonion Polynomials
• Skew-Polynomial Rings and Skew-Cyclic Codes
• Polynomial Equations over Octonion Algebras
• Standard Polynomial Equations over Division Algebras

Related

• Algebra of linear recurrence relations in arbitrary characteristic
• Recurrence matrices
• On Recurrence Relations of Multi-dimensional Sequences
• A Solution of Simultaneous Recurrences
• Division Algebras and Quadratic Reciprocity