Hafnian
In mathematics, the hafnian is a scalar function of a symmetric matrix that generalizes the permanent. The hafnian was named by Eduardo R. Caianiello "to mark the fruitful period of stay in Copenhagen (Hafnia in Latin)." == Definition == The hafnian of a 2 n × 2 n {\displaystyle 2n\times 2n} symmetric matrix A {\displaystyle A} is defined as haf ( A ) = ∑ ρ ∈ P 2 n 2 ∏ { i , j } ∈ ρ A i , j , {\displaystyle \operatorname {haf} (A)=\sum _{\rho \in P_{2n}^{2}}\prod _{\{i,j\}\in \rho }A_{i,j},} where P 2 n 2 {\displaystyle P_{2n}^{2}} is the set of all partitions of the set { 1 , 2 , … , 2 n } {\displaystyle \{1,2,\dots ,2n\}} into subsets of size 2 {\displaystyle 2} .