| Title:
|
On the $f$- and $h$-triangle of the barycentric subdivision of a simplicial complex (English) |
| Author:
|
Ahmad, Sarfraz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
989-994 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\mathop {\rm sd}(\Delta )$. (English) |
| Keyword:
|
symmetric group |
| Keyword:
|
simplicial complex |
| Keyword:
|
$f$- and $h$-vector (triangle) |
| Keyword:
|
barycentric subdivision of a simplicial complex |
| MSC:
|
05A05 |
| MSC:
|
05E40 |
| MSC:
|
05E45 |
| idZBL:
|
Zbl 1301.05004 |
| idMR:
|
MR3165509 |
| DOI:
|
10.1007/s10587-013-0066-5 |
| . |
| Date available:
|
2014-01-28T14:11:33Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143611 |
| . |
| Reference:
|
[1] Björner, A., Wachs, M. L.: Shellable nonpure complexes and posets I.Trans. Am. Math. Soc. 348 1299-1327 (1996). Zbl 0857.05102, MR 1333388, 10.1090/S0002-9947-96-01534-6 |
| Reference:
|
[2] Brenti, F., Welker, V.: $f$-vectors of barycentric subdivisions.Math. Z. 259 849-865 (2008). Zbl 1158.52013, MR 2403744, 10.1007/s00209-007-0251-z |
| Reference:
|
[3] Miller, E., Sturmfels, B.: Combinatorial Commutative Algebra.Graduate Texts in Mathematics 227 Springer, New York (2005). Zbl 1090.13001, MR 2110098 |
| Reference:
|
[4] Stanley, R. P.: Combinatorics and Commutative Algebra.Progress in Mathematics 41 Birkhäuser, Basel (1996). Zbl 0838.13008, MR 1453579 |
| . |
