For fixed degree d, strength and partition rank over any field are bounded by O(r^{d-1}) (plus a log factor on finite fields) in terms of their border rank analogues.
The set of forms with bounded strength is not closed
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Strength and partition rank under limits and field extensions
For fixed degree d, strength and partition rank over any field are bounded by O(r^{d-1}) (plus a log factor on finite fields) in terms of their border rank analogues.