The coalescence model based on nucleon distribution functions from an isospin-dependent transport model is used to study the production of light clusters such as deuteron, triton, and $^{3}$He from heavy-ion collisions induced by neutron-rich nuclei at intermediate energies. It is found that the emission time of light clusters depends on their masses. For clusters with the same momentum per nucleon, heavier ones are emitted earlier. Both the yield and energy spectrum of light clusters are sensitive to the density dependence of nuclear symmetry energy, with more light clusters produced in the case of a stiff symmetry energy. On the other hand, effects due to the stiffness of the isoscalar part of nuclear equation of state and the medium dependence of nucleon-nucleon cross sections on light cluster production are unimportant. We have also studied the correlation functions of clusters, and they are affected by the density dependence of nuclear symmetry energy as well, with the stiff symmetry energy giving a stronger anti-correlation of light clusters, particularly for those with large kinetic energies. Dependence of light cluster production on the centrality and incident energy of heavy ion collisions as well as masses of the reaction system is also investigated.
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