Some numerical results on Fekete polynomials

Some Numerical Results on Fekete Polynomials

It is known that if x is a real residue character modulo k with x(p) = — 1 k n for the first five primes p, then the corresponding Fekete polynomial £„=j X(n)x changes sign on (0, 1). In this paper it is shown that the condition that x(p) be — 1 for the first four primes p is not sufficient to guarantee such a sign change. More specifically, if x ¡s the real nonprincipal character modulo either...

Some results on the block numerical range

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.

Zeros of Fekete Polynomials

Some Results on the Field of Values of Matrix Polynomials

In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied.  Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of ...

Some Results on Chromatic Polynomials of Hypergraphs

In this paper, chromatic polynomials of (non-uniform) hypercycles, unicyclic hypergraphs, hypercacti and sunflower hypergraphs are presented. The formulae generalize known results for r-uniform hypergraphs due to Allagan, Borowiecki/ Lazuka, Dohmen and Tomescu. Furthermore, it is shown that the class of (non-uniform) hypertrees with m edges, where mr edges have size r, r ≥ 2, is chromatically c...