SPECTRAL PROPERTIES OF SOME MATRICES CLOSE TO THE TOEPLITZ TRIANGULARFORM

We consider a class of matrices, that we call nearly Toeplitz, and sho w that they have interesting spectral properties. More precisely, we s how that the eigenvectors of certain nearly Toeplitz matrices give com plete information about the structure of the symmetric group S(k), i.e ., the group of permutations of the integers 1,...,k. Obtaining this k ind of information is a central task in two seemingly unrelated branch es of mathematics, namely the Character Theory of the Symmetric Group and the Polya's Theory of Counting.