A note on the simultaneous Waring rank of monomials. (English) Zbl 1394.05141

Carlini, Enrico; Ventura, Emanuele

Ill. J. Math. 61, No. 3-4, 517-530 (2017).

Summary: In this paper, we study the complex simultaneous Waring rank for collections of monomials. For general collections, we provide a lower bound, whereas for special collections we provide a formula for the simultaneous Waring rank. Our approach is algebraic and combinatorial. We give an application to ranks of binomials and maximal simultaneous ranks. Moreover, we include an appendix of scripts written in the algebra software Macaulay2 to experiment with simultaneous ranks.

MSC:

05E15	Combinatorial aspects of groups and algebras (MSC2010)
05E40	Combinatorial aspects of commutative algebra

Keywords:

complex simultaneous Waring rank for collections of monomials

Software:

Macaulay2

References:

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