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Regular Sequences of Symmetric Polynomials by Conca, Aldo; Krattenthaler, Christian; Watanabe, Junzo is a scholarly article available to read on EtoBox.

What is Regular Sequences of Symmetric Polynomials about?

Denote by p_k the k-th power sum symmetric polynomial n variables. The interpretation of the q-analogue of the binomial coefficient as Hilbert function leads us to discover that n consecutive power sums in n variables form a regular sequence. We consider then the following problem: describe the subsets n powersums forming a regular sequence. A necessary condition is that n! divides the product of the degrees of the elements. To find an easily verifiable sufficient condition turns out to be surprisingly difficult already in 3 variables. Given positive integers a<b<c with GCD(a,b,c)=1, we conjecture that p_a, p_b, p_c is a regular sequence for n=3 if and only if 6 divides abc. We provide evidence for the conjecture by proving it in several special instances.

Author

Conca, Aldo; Krattenthaler, Christian; Watanabe, Junzo

Published

2008

Language

EN