Ryser Formula
The fastest known general exact algorithm is due to Herbert John Ryser (Ryser (1963)). Ryser’s method is based on an inclusion–exclusion formula that can be given as follows: Let be obtained from A by deleting k columns, let be the product of the row-sums of, and let be the sum of the values of over all possible . Then
It may be rewritten in terms of the matrix entries as follows
Ryser’s formula can be evaluated using arithmetic operations, or by processing the sets in Gray code order.
Read more about this topic: Computing The Permanent
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