Illinois Journal of Mathematics

A note on the simultaneous Waring rank of monomials

Enrico Carlini and Emanuele Ventura

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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.

Article information

Illinois J. Math., Volume 61, Number 3-4 (2017), 517-530.

Received: 27 November 2017
Revised: 7 May 2018
First available in Project Euclid: 22 August 2018

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Zentralblatt MATH identifier

Primary: 51N35: Questions of classical algebraic geometry [See also 14Nxx] 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 05E40: Combinatorial aspects of commutative algebra


Carlini, Enrico; Ventura, Emanuele. A note on the simultaneous Waring rank of monomials. Illinois J. Math. 61 (2017), no. 3-4, 517--530. doi:10.1215/ijm/1534924838.

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