2003/12/03 by Donald Mills, Mills, Donald, Kent M. Neuerburg +1
Computer Science · Mathematics · #12Y05 #13P99 #Advanced Combinatorial Mathematics #Coding theory and cryptography #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.RA #msc:12Y05 #msc:13P99
paper · pdf · doi:10.48550/arxiv.math/0312093
10 pages; to appear in Algebra Colloquium
arxiv created 2003/12/03 · openalex publication_date 2003/12/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of a composed product for univariate polynomials has been explored extensively by Brawley, Brown, Carlitz, Gao, Mills, et al. Starting with these fundamental ideas and utilizing fractional power series representation (in particular, the Puiseux expansion) of bivariate polynomials, we generalize the univariate results. We define a bivariate composed sum, composed multiplication, and composed product (based on function composition). Further, we investigate the algebraic structure of certain classes of bivariate polynomials under these operations. We also generalize a result of Brawley and Carlitz concerning the decomposition of polynomials into irreducibles.