We prove that the number of combinatorially distinct causal 3-dimensional
triangulations homeomorphic to the 3-dimensional sphere is bounded by an
exponential function of the number of tetrahedra. It is also proven that the
number of combinatorially distinct causal 4-dimensional triangulations
homeomorphic to the 4-sphere is bounded by an exponential function of the
number of 4-simplices provided the number of all combinatorially distinct
triangulations of the 3-sphere is bounded by an exponential function of the
number of tetrahedra.Comment: 30 pages, 9 figure
