Polynomial relations among the nth roots of one

On One-One Polynomial Time Equivalence Relations

Two sets A and B are one-one polynomial time equivalent (one-one p-equivalent) if there are polynomial time one-one reductions from A to B and from B to A. In this paper we show that all EXPTIME complete sets are one-one p-equivalent by length increasing reductions. Moreover we show this result for many complexity classes which can be proved by a straightforward diagonalization to contain P pro...

On the Roots of Hosoya Polynomial of a Graph

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

extensions of some polynomial inequalities to the polar derivative

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On the integrality of nth roots of generating functions

Motivated by the discovery that the eighth root of the theta series of the E8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ R (where R = 1 + xZ x ) can be written as f = gn for g ∈ R, n 2. Let Pn := {gn | g ∈R} and let μn := n∏p |n p. We show among other things that (i) for f ∈R, f ...

The Ecological Relations of Roots