Geodesic
On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 989-994

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For a simplicial complex $\Delta $ we study the behavior of its $f$- and $h$-triangle under the action of barycentric subdivision. In particular we describe the $f$- and $h$-triangle of its barycentric subdivision $\mathop {\rm sd}(\Delta )$. The same has been done for $f$- and $h$-vector of $\mathop {\rm sd}(\Delta )$ by F. Brenti, V. Welker (2008). As a consequence we show that if the entries of the $h$-triangle of $\Delta $ are nonnegative, then the entries of the $h$-triangle of $\mathop {\rm sd}(\Delta )$ are also nonnegative. We conclude with a few properties of the $h$-triangle of $\mathop {\rm sd}(\Delta )$.
DOI : 10.1007/s10587-013-0066-5
Classification : 05A05, 05E40, 05E45
Keywords: symmetric group; simplicial complex; $f$- and $h$-vector (triangle); barycentric subdivision of a simplicial complex 
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Ahmad, Sarfraz. On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 989-994. doi: 10.1007/s10587-013-0066-5

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