Conserved quantity associated with Permutation Symmetry?

Question

Based on my crude understanding of Noether's Theorem, for each symmetry in physics, there is a conserved quantity associated with it. If so, what is the conserved quantity associated with permutation symmetry?

Answer 1

Noether's theorem only gives conserved quantities for continuous symmetries, like rotation, not discrete rotations like permutations. See the question and answers here: Conserved quantity corresponding to reflection symmetry