Balanced Vertex Decomposable Simplicial Complexes and their h-vectors

@article{Biermann2013BalancedVD,
  title={Balanced Vertex Decomposable Simplicial Complexes and their h-vectors},
  author={Jennifer Biermann and Adam Van Tuyl},
  journal={Electron. J. Comb.},
  year={2013},
  volume={20},
  pages={P15}
}
Given any finite simplicial complex \Delta, we show how to construct a new simplicial complex \Delta_{\chi} that is balanced and vertex decomposable. Moreover, we show that the h-vector of the simplicial complex \Delta_{\chi} is precisely the f-vector, denoted f(\Delta), of the original complex \Delta. We deduce this result by relating f(\Delta) with the graded Betti numbers of the Alexander dual of \Delta_{\chi}. Our construction generalizes the "whiskering" construction of Villarreal, and… 

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