A sum sequence modulo n is a sequence S = ( s 1 , s 2 , … , s d ) of elements in Z / n Z such that every x ∈ Z / n Z can be represented as s i + s j , i < j , in the same number λ of ways. For example, ( 0 , 1 , 2 , 4 ) is a sum sequence modulo 6 with λ = 1 . We examine polynomials associated with sum sequences using tools from number theory, combinatorics and Galois theory. In particular, we give a complete characterization of sum sequences and their associated polynomials. We also describe some variations on these ideas and mention several possible generalizations to arbitrary finite groups.
原文链接
分享
引用
