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Exact strangeness conservation in heavy ion collisions

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.