Emanuele Delucchi ; Aaron Pixton ; Lucas Sabalka - $f$-vectors of subdivided simplicial complexes (extended abstract)

dmtcs:2822 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2822
$f$-vectors of subdivided simplicial complexes (extended abstract)Article

Authors: Emanuele Delucchi 1; Aaron Pixton 2; Lucas Sabalka 1

  • 1 Department of mathematical science
  • 2 Department of Mathematics - Princeton University

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.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: subdivisions of simplicial complexes,$f$-vectors,$f$-polynomials,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Consultation statistics

This page has been seen 163 times.
This article's PDF has been downloaded 270 times.