Discrete Mathematics & Theoretical Computer Science 
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.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0606356 Source : ScholeXplorer IsRelatedTo DOI 10.1007/s002090070251z Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0606356
