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arXiv · 1806.03823

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

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.

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Imran Anwar, Shaheen Nazir. 2018-06-11. The $f$- and $h$-vectors of Interval Subdivisions. https://doi.org/10.1016/j.jcta.2019.105124

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