Maximum Waring ranks of monomials

Abstract

We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.

9 pages. v2: Conjecture 4 is now Theorem 3. v3: Shortened exposition; restored discussion of non-monomial examples

References in corpus (2)

• An upper bound for the Waring rank of a form
• On the third secant variety

Cited by in corpus (3)

• Border Ranks of Monomials
• Power sum decompositions of defining equations of reflection arrangements
• Some examples of forms of high rank