14,484 research outputs found
On the unimodality of independence polynomials of some graphs
In this paper we study unimodality problems for the independence polynomial
of a graph, including unimodality, log-concavity and reality of zeros. We
establish recurrence relations and give factorizations of independence
polynomials for certain classes of graphs. As applications we settle some
unimodality conjectures and problems.Comment: 17 pages, to appear in European Journal of Combinatoric
Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude
We compute explicitly the four-particle amplitude in superstring theories by
using the hyperelliptic language and the newly obtained chiral measure of
D'Hoker and Phong. Although the algebra of the intermediate steps is a little
bit involved, we obtain a quite simple expression for the four-particle
amplitude. As expected, the integrand is independent of all the insertion
points. As an application of the obtained result, we show that the perturbative
correction to the term in type II superstring theories is vanishing
point-wise in (even) moduli space at two loops.Comment: v1, LaTex file, 33 pages; v2, 34 pages, add references and minor
correction
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