On Partial Barycentric Subdivision

Abstract

The $$l{\mathrm{th}}$$ partial barycentric subdivision is defined for a $$(d-1)$$ -dimensional simplicial complex $$\Delta $$ and studied along with its combinatorial and geometric aspects. We analyze the behavior of the f- and h-vector under the lth partial barycentric subdivision extending previous work of Brenti and Welker on the standard barycentric subdivision – the case $$l = d$$ . We discuss and provide properties of the transformation matrices sending the f- and h-vector of $$\Delta $$ to the f- and h-vector of its lth partial barycentric subdivision. We conclude with open problems.