1-dimensional representation

Alternating character

The alternating character or signature is a 1-dimensional irrep (i.e. linear character) and group homomorphism of a Symmetric group. #m/def/group It is given by

where is the number of 2-cycles in any decomposition of .

Proof of well-defined

#missing/proof

Properties

  1. is the Alternating group
  2. where is the crossing number of the Birdtrack notation of .

#state/tidy | #lang/en | #SemBr