2001/09/18 by V. M. Buchstaber, Victor Matveevich Buchstaber, E. G. Rees +3
Computer Science · Mathematics · #05A18 #14A05 #46E25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Polynomial and algebraic computation #math.AG #math.CO #math.FA #msc:05A18 #msc:14A05 #msc:46E25
paper · pdf · doi:10.48550/arxiv.math/0109122
14 pages, Latex
arxiv created 2001/09/18 · openalex publication_date 2001/09/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If A is an algebra of functions on X, there are many cases when X can be regarded as included in Hom(A,C) as the set of ring homomorphisms. In this paper the corresponding results for the symmetric products of X are introduced. It is shown that the symmetric product Symn(X) is included in Hom(A,C) as the set of those functions that satisfy equations generalising f(xy)=f(x)f(y). These equations are related to formulae introduced by Frobenius and, for the relevant A, they characterise linear maps on A that are the sum of ring homomorphisms. The main theorem is proved using an identity satisfied by partitions of finite sets.