On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex

Ahmad, Sarfraz. "On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex." Czechoslovak Mathematical Journal 63.4 (2013): 989-994. <http://eudml.org/doc/260827>.

@article{Ahmad2013,
abstract = {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 $\mathop \{\rm sd\}(\Delta )$.},
author = {Ahmad, Sarfraz},
journal = {Czechoslovak Mathematical Journal},
keywords = {symmetric group; simplicial complex; $f$- and $h$-vector (triangle); barycentric subdivision of a simplicial complex; symmetric group; simplicial complex; -vector; -vector; barycentric subdivision},
language = {eng},
number = {4},
pages = {989-994},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex},
url = {http://eudml.org/doc/260827},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Ahmad, Sarfraz
TI - On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 4
SP - 989
EP - 994
AB - 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 $\mathop {\rm sd}(\Delta )$.
LA - eng
KW - symmetric group; simplicial complex; $f$- and $h$-vector (triangle); barycentric subdivision of a simplicial complex; symmetric group; simplicial complex; -vector; -vector; barycentric subdivision
UR - http://eudml.org/doc/260827
ER -