Del permanente de una matriz

Abstract

The mathematician Agustin-Louis Cauchy in his famous 84-page memory develops the theory of determinants as a special type of alternating symmetric functions, which he distinguished from ordinary symmetric functions by calling these last permanent symmetric functions. He also introduced a certain subclass of symmetric functions that were later called permanent by the Scottish mathematician Sir Thomas Muir and that today are known by this name. This function, the permanent function can be written in a very similar way to the determinant and thanks to this similarity one would expect the permanent to have properties analogous to the properties of the determinant. Unfortunately, the permanent one fail to inherit key properties and this deficiency explains the fact that proof of permanent's theorems and their calculation is substantially much more difficult.