Abstract
The lth partial barycentric subdivision is defined for a (d-1)-dimensional simplicial complex Δand studied along with its combinatorial, geometric and algebraic 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 = 1. We discuss and provide properties of the transformation matrices sending the f- and h-vector of Δto the f- and h-vector of its lth partial barycentric subdivision. We conclude with open problems.
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