2020/03/30 by Athanasiadis, Christos A.
#05A05 #05E45 #26C10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2003.13372
A triangulation of a simplicial complex Δ is called uniform if the f-vector of its restriction to a face of Δ depends only on the dimension of that face. This paper proves that the entries of the h-vector of a uniform triangulation of Δ can be expressed as nonnegative integer linear combinations of those of the h-vector of Δ, where the coefficients depend only on the dimension of Δ and the f-vectors of the restrictions of the triangulation to simplices of various dimensions. Moreover, it provides information about these coefficients, including formulas, recurrence relations and various interpretations, and gives a criterion for the h-polynomial of a uniform triangulation to be real-rooted. These results unify and generalize several results in the literature about special types of triangulations, such as barycentric, edgewise and interval subdivisions.