Face Numbers of Uniform Triangulations of Simplicial Complexes

Abstract A triangulation of a simplicial complex $\Delta $ is said to be uniform if the $f$-vector its restriction face depends only on dimension that face. This paper proves entries $h$-vector can expressed as nonnegative integer linear combinations those $, where coefficients depend and $f$-vectors restrictions simplices various dimensions. Furthermore, it provides information about these coefficients, including formulas, recurrence relations, interpretations, gives criterion for $h$-polynomial real rooted. These results unify generalize several in literature special types triangulations, such barycentric, edgewise interval subdivisions.