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 $\mathbb{C}[x_1,x_2,\dots,x_n]$ for $n \geq 3$ 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 $\mathbb{C}[x_1,x_2,x_3,x_4]$. 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 $p_{a}, p_{a+1},\dots, p_{a+ m-1},p_b$ with $m <n-1$ forms a regular sequence in $\mathbb{C}[x_1,x_2,\dots,x_n]$. We also provide a partial evidence in support of conjecture's given by Conca, Krattenthaler and Watanabe on regular sequences of symmetric polynomials.

Regular sequences of power sums and complete symmetric polynomials

KUMAR, NEERAJ;
2012-01-01

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 $\mathbb{C}[x_1,x_2,\dots,x_n]$ for $n \geq 3$ always form a regular sequence and we state the conjecture when $p_a,p_b,p_c$ for given positive integers $a
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/776848
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact