1. On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex
- Creator:
- Ahmad, Sarfraz
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- symmetric group, simplicial complex, $f$- and $h$-vector (triangle), and barycentric subdivision of a simplicial complex
- Language:
- English
- Description:
- 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 $\mathop {\rm sd}(\Delta )$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public