We establish a general and optimal lower bound for the complete sum of the probabilities of k-intersections of n events. We then describe various applications to additive and multiplicative number theory, graph theory, coding theory, study of lattice points on circles, and divisors of polynomials.
[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
@article{urn:eudml:doc:41916,
title = {An overlapping theorem with applications.},
journal = {Publicacions Matem\`atiques},
year = {2007},
pages = {107-118},
zbl = {1165.60304},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41916}
}
Cilleruelo, Javier; Tenenbaum, Gérald. An overlapping theorem with applications.. Publicacions Matemàtiques, (2007), pp. 107-118. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41916/