一类非线性对称方程组解集的结构

The Structure of Solution of Non-linear Symmetrical Equation Sets

主要讨论了非线性对称方程组Ｓ１＝Ｓ２＝…Ｓ２＝…＝Ｓλ－１＝Ｓλ＋１＝…＝Ｓｎ＝Ｓｎ＋１（１≤λ≤ｎ），（Ｓｋ＝ｘ１ｋ＋ｘ２ｋ＋…＋ｘｎｋ，ｋ＝０，１，２，…）的非零解，并指出其解集的结构．

This paper mainly discusses the non-zero solution of non-linear symmetrical equation sets of S1=S2…=Sλ_1 = Sλ+１=…=Sn= Sn +1,(1≤λ≤ｎ),(Sk= x1k+x2k+…xnk,k =0,1,2,…） and points out the structure of the solution sets.