Charged kaon production has been measured in Si+Al and Si+Au collisions at 14.6 A GeV/c, and Au+Au collisions at 11.1 A GeV/c by Experiments 859 and 866 (the E--802 Collaboration) at the BNL AGS. Invariant transverse mass spectra and rapidity distributions for both K+ and K- are presented. The centrality dependence of rapidity-integrated kaon yields is studied. Strangeness enhancement is observed as an increase in the slope of the kaon yield with the total number of participants as well as the yield per participant. The enhancement starts with peripheral Si+Al and Si+Au collisions (relative to N+N) and appears to saturate for a moderate number of participating nucleons in Si+Au collisions. It is also observed to increase slowly with centrality in Au+Au collisions, to a level in the most central Au+Au collisions that is greater than that found in central Si+A collisions. The enhancement factor for $K^+$ production are 3.0 +-0.2(stat.) +-0.4(syst.) and 4.0 +-0.3(stat.) +-0.5(syst.), respectively, for the most central 7% Si+Au collisions and the most central 4% Au+Au collisions relative to N+N at the correponding beam energy.
In this paper Au+Au collisions at 11.6A GeV/c are characterized by two global observables: the energy measured near zero degrees (EZCAL) and the total event multiplicity. Particle spectra are measured for different event classes that are defined in a two-dimensional grid of both global observables. For moderately central events (σ/σint<12%) the proton dN/dy distributions do not depend on EZCAL but only on the event multiplicity. In contrast the shape of the proton transverse spectra shows little dependence on the event multiplicity. The change in the proton dN/dy distributions suggests that different conditions are formed in the collision for different event classes. These event classes are studied for signals of new physics by measuring pion and kaon spectra and yields. In the event classes doubly selected on EZCAL and multiplicity there is no indication of any unusual pion or kaon yields, spectra, or K/π ratio even in the events with extreme multiplicity.