HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# $f$-vectors of subdivided simplicial complexes (extended abstract)

Abstract : We take a geometric point of view on the recent result by Brenti and Welker, who showed that the roots of the $f$-polynomials of successive barycentric subdivisions of a finite simplicial complex $X$ converge to fixed values depending only on the dimension of $X$. We show that these numbers are roots of a certain polynomial whose coefficients can be computed explicitly. We observe and prove an interesting symmetry of these roots about the real number $-2$. This symmetry can be seen via a nice realization of barycentric subdivision as a simple map on formal power series. We then examine how such a symmetry extends to more general types of subdivisions. The generalization is formulated in terms of an operator on the (formal) ring on the set of simplices of the complex.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [4 references]

https://hal.inria.fr/hal-01186250
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 24, 2015 - 3:45:00 PM
Last modification on : Tuesday, October 19, 2021 - 12:50:52 PM
Long-term archiving on: : Wednesday, November 25, 2015 - 4:52:06 PM

### File

dmAN0149.pdf
Publisher files allowed on an open archive

### Citation

Emanuele Delucchi, Aaron Pixton, Lucas Sabalka. $f$-vectors of subdivided simplicial complexes (extended abstract). 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.693-700, ⟨10.46298/dmtcs.2822⟩. ⟨hal-01186250⟩

Record views