I am not sure if the following question falls within the scope of this site; if it does not, I will request the moderators to take appropriate actionI have been going through Jin-Yi Cai's expository paper on Holographic algorithms.I had a question. Immediately after introducing Grassman-Plucker Identities for Pfaffians and the definitions for matchgates, recognizers and generators, Cai introduces signature tensor for matchgates.My question arises from the following statement.He states that a generator $\Gamma$ with $m$ output nodes is assigned a contravariant tensor $\mathbf{G} \in V_0^m$ of type $\binom {m} {0}$.I looked up contravariant tensors on wikipedia but did not find any reference to the type of contravariant tensors which Cai talks about. Maybe I am not searching properly, but I was unable to find a proper reference which defines what I am looking for.I would be glad if anyone could help me with this.Thanks-Akash
What are contravariant tensors of type m choose 0
terminology;tensor rank