- #1
sgd37
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Homework Statement
Having a symmetric tensor [tex] S^{a_1 ...a_n} [/tex] forming a vector space [tex] V_n [/tex] with indices taking values from 1 to 3; what is the dimension of such a vector space?
Homework Equations
The Attempt at a Solution
essentially this reduces to picking a tensor of type [tex] S^{ \underbrace{1...1}_{s} \underbrace{2...2}_{r} \underbrace{3...3}_{t}}[/tex] with r+s+t =n and seeing how many non isomorphic combinations there are. I'm not that skilled at combinatorics unfortunately