Interlacing methods and large indecomposables

The Extended Module of Indecomposables

We construct a generalization of the usual module of indecomposables for the mod 2 cohomology of a finite //-space. Structure theorems are obtained regarding how the Steenrod algebra acts on this module.

Polynomials , roots , and interlacing

Interlacing Eigenvalues and Graphs

We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of a maximal (colclique, the chromatic number, the diameter, and the bandwidth, in terms of the eigenvalues of the Standard adjacency matrix or the Laplacian matrix. We also deal with inequalities and regularity resu...

Separation and Interlacing Theorems

Self-interlacing polynomials II: Matrices with self-interlacing spectrum

An n×n matrix is said to have a self-interlacing spectrum if its eigenvalues λk , k = 1, . . . ,n, are distributed as follows: λ1 >−λ2 > λ3 > · · ·> (−1)λn > 0. A method for constructing sign definite matrices with self-interlacing spectrum from totally nonnegative ones is presented. This method is applied to bidiagonal and tridiagonal matrices. In particular, a result by O. Holtz on the spectr...