**Author(s): ** Neeraj Kumar |

Ivan Martino**Journal: ** Le Matematiche ISSN 0373-3505

**Volume: ** 67;

**Issue: ** 1;

**Start page: ** 103;

**Date: ** 2012;

Original page**Keywords: ** Regular sequences |

Symmetric polynomials**ABSTRACT**

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 ≥ 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.

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