%0 Journal Article
%T Regular sequences of power sums and complete symmetric polynomials
%A Neeraj Kumar
%A Ivan Martino
%J Le Matematiche
%D 2012
%I University of Catania
%X In this article, we carry out the investigation for regular sequences of symmetric polynomials in the polynomial ring in three and four variable. Any two power sum element in C[x_1, x_2, . . . , x_n] for n ¡Ý 3 always form a regular sequence and we state the conjecture when p_a, p_b, p_c for given positive integers a < b < c forms a regular sequence in C[x_1, x_2, x_3, x_4 ]. We also provide evidence for this conjecture by proving it in special instances. We also prove that any sequence of power sums of the form p_a, p_a+1 , . . ., p_a+m 1 , p_b with m < n   1 forms a regular sequence in C[x_1, x_2, . . . , x_n ]. We also provide a partial evidence in support of conjecture¡¯s given by Conca, Krattenthaler and Watanble in [1] on regular sequences of symmetric polynomials.
%K Regular sequences
%K Symmetric polynomials
%U http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/945