  We investigate the increase in strangeness production with charged particle
multiplicity ($dN_{ch}/dy$) seen by the ALICE collaboration at CERN in p-p,
p-Pb and Pb-Pb collisions using the hadron resonance gas model. The strangeness
canonical ensemble is used taking into account the interactions among hadrons
using S-matrix corrections based on known phase shift analyses. We show the
essential role of constraints due to the exact conservation of strangeness
which is instrumental to describing observed features of strange particle
yields and their scaling with $dN_{ch}/dy$. Furthermore, the results on
comparing the hadron resonance gas model with and without S-matrix corrections,
are presented. We observe that the interactions introduced by the phase shift
analysis via the S-matrix formalism are essential for a better description of
the yields data independent of collision system. This work is based on our
long-lasting collaboration and most recent publications with Jean Cleymans.
