2012/09/12 by Ahmad, Sarfraz, Welker, Volkmar
#05A05 #05E45 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1209.2581
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.