Irreducibility of Hypersurfaces

Irreducibility of Hypersurfaces

Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most deg(P ) − 1 values of the coefficient. We more generally handle the situation where several specified coefficients vary.

Clique Irreducibility and Clique Vertex Irreducibility of Graphs

A graphs G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irred...

Irreducibility of Hecke Polynomials

In this note, we show that if the characteristic polynomial of some Hecke operator Tn acting on the space of weight k cusp forms for the group SL2(Z ) is irreducible, then the same holds for Tp, where p runs through a density one set of primes. This proves that if Maeda’s conjecture is true for some Tn, then it is true for Tp for almost all primes p.

Stochastic Irreducibility Of Spin

The Irreducibility of Consciousness

In this paper, by analyzing the Chalmers-Searle debate about Chalmers’ zombie thought experiment, I attempt to determine the implications that the irreducibility of consciousness has for the truth of materialism. While Chalmers claims that the irreducibility of consciousness forces us to embrace dualism, Searle claims that it has no deep metaphysical im­ port and, in particular, that it is full...