An analog of a Determinant where all the signs in the expansion by Minors are taken as Positive. The
permanent of a Matrix *A* is the coefficient of in

(Vardi 1991). Another equation is the Ryser Formula

where the Sum is over all Subsets of , and is the number of elements in (Vardi 1991).

If
is a Unitary Matrix, then

(Minc 1978, p. 25; Vardi 1991).

**References**

Borovskikh, Y. V. and Korolyuk, V. S. *Random Permanents.* Philadelphia, PA: Coronet Books, 1994.

Minc, H. *Permanents.* Reading, MA: Addison-Wesley, 1978.

Vardi, I. ``Permanents.'' §6.1 in *Computational Recreations in Mathematica.*
Reading, MA: Addison-Wesley, pp. 108 and 110-112, 1991.

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1999-05-26