Meaning of totally antisymmetric tensor

[homology]

Simple question I am confused on. If I have a tensor M^{\alpha\beta\gamma} that is totally antisymmetric in its indices then is it the case that M changes sign under the exchange of any two indices? And as a followup, a totally symmetric tensor has no sign changes on any pair exchange of indices?

Thanks,

Kevin

 

[quasar987]

What is your definition of a tensor, and of a totally antisymmetric tensor (resp. totally symmetric tensor)?

 

[M Quack]

Take a look at the Levi-Civita symbol

http://en.wikipedia.org/wiki/Levi-Civita_symbol

 

[homology]

Damn I think I figured out my problem. I was going off Carroll's definition/discussion of (anti-) symmetry (Spacetime and Geometry) which implies that an exchange of a pair of indices in a totally antisymmetric tensor yields a sign change. This is fine I realize now, what is not fine is the following.

I was looking at \partial_{\alpha}F_{\beta\gamma}. I know that \partial_{\[\alpha}F_{\beta\gamma\]}=0 and I then INCORRECTLY assumed that \partial_{\alpha}F_{\beta\gamma} was totally symmetric which was leading me into errors...argh...noob mistake.