On $\g$- and local $\g$-Vectors of the Interval Subdivision

Imran Anwar; Shaheen Nazir

On $\g$- and local $\g$-Vectors of the Interval Subdivision

Commutative Algebra 2018-07-10 v1

Authors: Imran Anwar , Shaheen Nazir

Abstract

We show that the $\g$ -vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric $h$ -vector is nonnegative. In particular, we prove that such $\g$ -vector is the $f$ -vector of some balanced simplicial complex. Moreover, we show that the local $\g$ -vector of the interval subdivision of a simplex is nonnegative; answering a question by Juhnke-Kubitzke et al.

Keywords

g-vector local g-vector interval subdivision simplicial complex h-vector balanced complex

Cite

@article{arxiv.1807.02806,
  title  = {On $\g$- and local $\g$-Vectors of the Interval Subdivision},
  author = {Imran Anwar and Shaheen Nazir},
  journal= {arXiv preprint arXiv:1807.02806},
  year   = {2018}
}

Comments

20 pages,1 figure

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