Strangeness enhancement at mid-rapidity in Pb-Pb collisions at 158 GeV/c

$K^{0}_{s}$, $\Lambda$, $\Xi$, $\Omega$ and negative particle yields and transverse mass spectra have been measured at central rapidity in Pb-Pb and p-Pb collisions at 158 $A$ GeV/$c$. The yields in Pb-Pb interactions % are presented as a function of the collision centrality and compared with those obtained from p-Pb collisions. Strangeness enhancement in Pb-Pb relative to p-Pb collisions increases with the strangeness content of the particle. Going from p-Pb to Pb-Pb, the strange particle yields increase faster than linearly with the number of participants $N_{part}$ up to $N_{part} \approx 100$, thereafter the increase becomes %linear with $N_{part}$. Yields are studied as a function of the number of nucleons participating in the collision $N_{part}$, which is estimated with the Glauber model. From p-Pb to Pb-Pb collisions the particle yields per participant increase substantially. The enhancement is more pronounced for multistrange particles, and exceeds an order of magnitude for the $\Omega$. For a number of participants, $N_{part}$, greater than $100$, however, all yields per participant appear to be constant.