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

**References**

Littlewood, D. E. and Richardson, A. R. ``Group Characters and Algebra.'' *Philos. Trans. Roy. Soc. London A* **233**, 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.

© 1996-9

1999-05-26