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Constraining the high-density behavior of nuclear equation of state from strangeness production in heavy-ion collisions

The dynamics of pions and strange particles in heavy-ion collisions in the region of 1A GeV energies is investigated by the lanzhou quantum molecular dynamics model for probing the nuclear equation of state at supra-saturation densities. The total multiplicities and the ratios obtained in $^{197}$Au+$^{197}$Au over $^{12}$C+$^{12}$C systems are calculated for selected Skyrme parameters SkP, SLy6, Ska and SIII, which correspond to different modulus of incompressibility of symmetric nuclear matter and different cases of the stiffness of symmetry energy. A decrease trend of the excitation functions of the ratios for strange particle production with increasing incident energy was observed. The available data of K$^{+}$ production measured by KaoS collaboration are described well with the parameter SkP, which results in a soft equation of state. The conclusions can not be modified by an in-medium kaon-nucleon potential.