Permanent

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. Both permanent and determinant are special cases of a more general function of a matrix called the immanant.

Definition

The permanent of an n-by-n matrix A = (a_i,j) is defined as

The sum here extends over all elements σ of the symmetric group S_n; i.e. over all permutations of the numbers 1, 2, ..., n.

For example,

and

The definition of the permanent of A differs from that of the determinant of A in that the signatures of the permutations are not taken into account.

The permanent of a matrix A is denoted per A, perm A, or Per A, sometimes with parentheses around the argument. In his monograph, Minc (1984) uses Per(A) for the permanent of rectangular matrices, and uses per(A) when A is a square matrix. Muir (1882) uses the notation .

The word, permanent, originated with Cauchy in 1812 as “fonctions symétriques permanentes” for a related type of function, and was used by Muir (1882) in the modern, more specific, sense.

The Man

"The Man" is a slang phrase that may refer to the government or to some other authority in a position of power. In addition to this derogatory connotation, it may also serve as a term of respect and praise.

The phrase "the Man is keeping me down" is commonly used to describe oppression. The phrase "stick it to the Man" encourages resistance to authority, and essentially means "fight back" or "resist", either passively, openly or via sabotage.

History

As a phrase meaning "the boss" it dates from at least 1918.

In the Southern U.S. states, the phrase came to be applied to any man or any group in a position of authority, or to authority in the abstract. From about the 1950s the phrase was also an underworld code word for police, the warden of a prison or other law enforcement or penal authorities.

The use of this term was expanded to counterculture groups and their battles against authority, such as the Yippies, which, according to a May 19, 1969 article in U.S. News and World Report, had the "avowed aim ... to destroy 'The Man', their term for the present system of government". The term eventually found its way into humorous usage, such as in a December 1979 motorcycle ad from the magazine Easyriders which featured the tagline, "California residents: Add 6% sales tax for The Man."