# Local h-Vectors of Quasi-Geometric and Barycentric Subdivisions

Martina Juhnke-Kubitzke, Satoshi Murai, Richard Sieg

Research output: Contribution to journalArticle

### Abstract

In this paper, we answer two questions on local h-vectors, which were asked by Athanasiadis. First, we characterize all possible local h-vectors of quasi-geometric subdivisions of a simplex. Second, we prove that the local (Formula presented.)-vector of the barycentric subdivision of any CW-regular subdivision of a simplex is nonnegative. Along the way, we derive a new recurrence formula for the derangement polynomials.

Original language English 1-16 16 Discrete and Computational Geometry https://doi.org/10.1007/s00454-018-9986-z Accepted/In press - 2018 Apr 2

### Fingerprint

Barycentric Subdivision
H-vector
Subdivision
Recurrence Formula
Rearrangement
Non-negative
Polynomials
Polynomial

### Keywords

• $$\gamma$$γ-vector
• Barycentric subdivision
• Local h-vector
• Quasi-geometric subdivision

### ASJC Scopus subject areas

• Theoretical Computer Science
• Geometry and Topology
• Discrete Mathematics and Combinatorics
• Computational Theory and Mathematics

### Cite this

Local h-Vectors of Quasi-Geometric and Barycentric Subdivisions. / Juhnke-Kubitzke, Martina; Murai, Satoshi; Sieg, Richard.

In: Discrete and Computational Geometry, 02.04.2018, p. 1-16.

Research output: Contribution to journalArticle

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