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Mathematics > Commutative Algebra

arXiv:1806.03823 (math)
[Submitted on 11 Jun 2018 (v1), last revised 1 Aug 2019 (this version, v2)]

Title:The $f$- and $h$-vectors of Interval Subdivisions

Authors:Imran Anwar, Shaheen Nazir
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Abstract:The interval subdivision Int$(\Delta)$ of a simplicial complex $\Delta$ was introduced by Walker. We give the complete combinatorial description of the entries of the transformation matrices from the $f$- and $h$-vectors of $\Delta$ to the $f$- and $h$-vectors of Int$(\Delta)$. We show that if $\Delta$ has non-negative $h$-vector then the $h$-polynomial of its interval subdivision has only real roots. As a consequence, we prove the Charney-Davis conjecture for Int$(\Delta)$, if $\Delta$ has non-negative reciprocal $h$-vector.
Comments: 17 pages, 1 figure
Subjects: Commutative Algebra (math.AC); Combinatorics (math.CO)
Cite as: arXiv:1806.03823 [math.AC]
  (or arXiv:1806.03823v2 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.1806.03823
Journal reference: J. Combin. Theory Ser. A 169, (2020), 105 -124
Related DOI: https://doi.org/10.1016/j.jcta.2019.105124

Submission history

From: Imran Anwar [view email]
[v1] Mon, 11 Jun 2018 06:24:08 UTC (38 KB)
[v2] Thu, 1 Aug 2019 09:13:17 UTC (18 KB)
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