Toeplitz minors and specializations of skew Schur polynomials

We express minors of Toeplitz matrices of finite and large dimension in terms of symmetric functions. Comparing the resulting expressions with the inverses of some Toeplitz matrices, we obtain explicit formulas for a Selberg-Morris integral and for specializations of certain skew Schur polynomials.Comment: v2: Added new results on specializations of skew Schur polynomials, abstract and title modified accordingly and references added; v3: final, published version; 18 page

The inverse of a tridiagonal kk-Toeplitz matrix

An square matrix is $k$-Toeplitz if its diagonals are periodic sequences of period $k$. We find rational formulas for the determinant, the characteristic polynomial, and the elements of the inverse of a tridiagonal $k$-Toeplitz matrix (in particular, of any tridiagonal matrix) over any commutative unital ring, using only elementary linear algebra.Comment: 15 page

Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix

Peer ReviewedPostprint (author's final draft