TY - JOUR
T1 - Local h-Vectors of Quasi-Geometric and Barycentric Subdivisions
AU - Juhnke-Kubitzke, Martina
AU - Murai, Satoshi
AU - Sieg, Richard
N1 - Funding Information:
Acknowledgements 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.
Funding Information:
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.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - 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 γ-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.
AB - 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 γ-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.
KW - Barycentric subdivision
KW - Local h-vector
KW - Quasi-geometric subdivision
KW - γ-vector
UR - http://www.scopus.com/inward/record.url?scp=85044756433&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044756433&partnerID=8YFLogxK
U2 - 10.1007/s00454-018-9986-z
DO - 10.1007/s00454-018-9986-z
M3 - Article
AN - SCOPUS:85044756433
SN - 0179-5376
VL - 61
SP - 364
EP - 379
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 2
ER -