Vol. 313, No. 2, 2021

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The Waring rank of binary binomial forms

Laura Brustenga i Moncusí and Shreedevi K. Masuti

Vol. 313 (2021), No. 2, 327–342
DOI: 10.2140/pjm.2021.313.327
Abstract

We give an explicit formula for the Waring rank of every binary binomial form with complex coefficients. We give several examples to illustrate this, and compare the Waring rank and the real Waring rank for binary binomial forms.

Keywords
Waring problem, Sylvester algorithm, perp ideal, Hilbert function, secant varieties, apolarity theory
Mathematical Subject Classification 2010
Primary: 13F20
Secondary: 11P05, 14N05
Milestones
Received: 17 January 2020
Revised: 22 June 2021
Accepted: 27 June 2021
Published: 12 October 2021
Authors
Laura Brustenga i Moncusí
Department of Mathematical Sciences
Univertisy of Copenhagen
Copenhagen
Denmark
Shreedevi K. Masuti
Department of Mathematics
Indian Institute of Technology Dharwad
WALMI Campus
Dharwad
Karnataka
India