Avviso di seminario:


Speaker: Federico Poloni (Università di Pisa)
Date: Tuesday 2017-10-31
Time: 11:00
Place: Sala Seminari Ovest, Dipartimento di Informatica
Title: Counting Fiedler pencils using diagrams

Fiedler pencils are a family of matrix pencils which generalizes the
well-known companion matrix: they are *linearizations*, i.e., they
provide a method to construct, given a matrix polynomial, a linear
eigenvalue problem with the same eigenvalues and multiplicities.

Fiedler pencils are constructed as products of special block matrices
that act nontrivially only on two contiguous blocks. They have a rich
structure that give rise to many combinatorial properties.

In this talk, we introduce a notation that associates to each pencil a
diagram that depicts its action on the blocks. Using this notation, we
can obtain visual proofs of several statements in the theory, and we can
solve several counting properties (such as "how many distinct Fiedler
pencils with repetitions of a given dimension exist"). Among them, in
particular, we are interested in counting Fiedler pencils associated to
symmetric and palindromic matrix polynomials which preserve the same
structure.

This talk is based on a joint work with Gianna Del Corso.