Discrete & Computational Geometry

, Volume 61, Issue 2, pp 364–379 | Cite as

Local h-Vectors of Quasi-Geometric and Barycentric Subdivisions

  • Martina Juhnke-KubitzkeEmail author
  • Satoshi Murai
  • Richard Sieg


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 \(\gamma \)-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.


Local h-vector \(\gamma \)-vector Barycentric subdivision Quasi-geometric subdivision 

Mathematics Subject Classification

05E45 05A05 



We wish to thank Christos Athanasiadis for his useful comments. The third author wants to express his gratitude to Isabella Novik for her hospitality at the University of Washington and interesting discussions about the subject. We would like to thank the reviewers for useful comments, especially for pointing out the result in Remark 4.8. The first and the third author were partially supported by the German Research Council DFG-GRK 1916. The second author was partially supported by JSPS KAKENHI JP16K05102.


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Authors and Affiliations

  1. 1.FB Mathematik/ InformatikUniversität OsnabrückOsnabrückGermany
  2. 2.Department of Mathematics, School of EducationWaseda UniversityShinjukuJapan

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