For an matrix, let denote any permutation , ,
..., of the set of numbers 1, 2, ..., , and let be the character of the symmetric group corresponding
to the partition .
Then the immanant
is defined as
where the summation is over the permutations of the symmetric
group and
Littlewood, D. E. and Richardson, A. R. "Group Characters and Algebra." Philos. Trans. Roy. Soc. London A233,
99-141, 1934.Littlewood, D. E. and Richardson, A. R. "Immanants
of Some Special Matrices." Quart. J. Math. (Oxford)5, 269-282,
1934.Wybourne, B. G. "Immanants of Matrices." §2.19
in Symmetry
Principles and Atomic Spectroscopy. New York: Wiley, pp. 12-13, 1970.
matrix, let 
denote any permutation 
, 
,
..., 
of the set of numbers 1, 2, ..., 
, and let 
be the character of the symmetric group corresponding
to the partition 
.
Then the immanant 
is defined as
permutations of the symmetric
group and
