Chromatic numbers, Buchstaber numbers and chordality of Bier spheres
Abstract
We describe all the Bier spheres of dimension $d$ with chromatic number equal to $d+1$ and prove that all other $d$-dimensional Bier spheres have chromatic number equal to $d+2$, for any integer $d\geq 0$. Then we prove a general formula for complex and mod $p$ Buchstaber numbers of a Bier sphere $\mathrm{Bier}(K)$, for each prime $p\in\mathbb{N}$ in terms of the $f$-vector of the underlying simplicial complex $K$. Finally, we classify all chordal Bier spheres and obtain their canonical realizations as boundaries of stacked polytopes.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Advanced Combinatorial Mathematics
Advanced Mathematical Identities
Publication details
- Journal / source
- Discrete Mathematics
- Volume
- 349
- Issue
- 9
- Pages
- 115189–115189
- Publication date
- 29 April 2026
- Language
- EN