A note on the simultaneous Waring rank of monomials

2017/10/31 by Carlini, Enrico, Ventura, Emanuele
#05E15 #05E40 #51N35 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.00089

Abstract

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.

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