Local h-Vectors of Quasi-Geometric and Barycentric Subdivisions
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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.
KeywordsLocal h-vector \(\gamma \)-vector Barycentric subdivision Quasi-geometric subdivision
Mathematics Subject Classification05E45 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.
- 1.Ahmad, V., Welker, S.: On partial barycentric subdivision. Results Math. 73(1). Art. No. 21 (2018)Google Scholar
- 5.Athanasiadis, C.A., Savvidou, C.: The local \(h\)-vector of the cluster subdivision of a simplex. Sém. Lothar. Combin. 66. Art. No. B66c (2011/2012)Google Scholar