In this paper, we recover the characteristic polynomial of an arrangement of hyperplanes by computing the rational equivalence class of the variety defined by the logarithmic ideal of the arrangement. The logarithmic ideal was introduced in [CDFV] in a study of the critical points of the master function. The above result is used to understand the asymptotic behaviour the Hilbert series of the l...

Let G be a mixed graph and L(G) be the Laplacian matrix of G. In this paper, the coefficients of the Laplacian characteristic polynomial of G are studied. The first derivative of the characteristic polynomial of L(G) is explicitly expressed by means of Laplacian characteristic polynomials of its edge deleted subgraphs. As a consequence, it is shown that the Laplacian characteristic polynomial o...

In this paper, we study the ε-lemniscate of the characteristic polynomial in relation to the pseudospectrum of the associated matrix. It is natural to investigate this question because these two sets can be seen as generalizations of eigenvalues. The question of numerical determination of the ε-lemniscate raises the problem of computing the characteristic polynomial p. We can express the coeffi...

In this paper, a general way to determine the adjacency graph of linear feedback shift registers (LFSRs) with characteristic polynomial (1 + x)c(x) from the adjacency graph of LFSR with characteristic polynomial c(x) is discussed, where c(x) can be any polynomial. As an application, the adjacency graph of LFSRs with characteristic polynomial (1+ x)p(x) are determined, where p(x) is a primitive ...

Let A be a supersingular abelian variety over a finite field k which is k-isogenous to a power of a simple abelian variety over k. Write the characteristic polynomial of the Frobenius endomorphism of A relative to k as f = g for a monic irreducible polynomial g and a positive integer e. We show that the group of k-rational points A(k) on A is isomorphic to (Z g(1) Z) unless A's simple component...