English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A symmetric tensor may be regarded as a partially symmetric tensor in severaldifferent ways. These produce different notions of rank for the symmetrictensor which are related by chains of inequalities. By exploiting algebraictools such as apolarity theory, we show how the study of the simultaneoussymmetric rank of partial derivatives of the homogeneous polynomial associatedto the symmetric tensor can be used to prove equalities among differentpartially symmetric ranks. This approach aims to understand to what extent thesymmetries of a tensor affect its rank. We apply this to the special cases ofbinary forms, ternary and quaternary cubics, monomials, and elementarysymmetric polynomials.

Partially symmetric variants of Comon's problem via simultaneous rank