The Levi-Civita symbol, denoted as \(\epsilon_{ijk}\) in three dimensions or \(\epsilon_{i_1 i_2 \ldots i_n}\) in \(n\) dimensions, is a mathematical object used in tensor analysis and differential geometry.
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Definition:
- odd permutation: -1
- even permutation: 1
- not a permutation: 0. This happens iff two more more indices are repeated