English

An Efficient Algebraic Criterion for Shellability

Commutative Algebra 2017-12-15 v3 Algebraic Geometry

Abstract

In this paper, we give a new and efficient algebraic criterion for the pure as well as non-pure shellability of simplicial complex Δ\Delta over [n]. We also give an algebraic characterization of a leaf in a simplicial complex (defined in [8]). Moreover, we introduce the concept of Gallai-simplicial complex ΔΓ(G)\Delta_{\Gamma}(G) of a finite simple graph G. As an application, we show that the face ring of the Gallai simplicial complex associated to tree is Cohen-Macaulay.

Keywords

Cite

@article{arxiv.1705.09537,
  title  = {An Efficient Algebraic Criterion for Shellability},
  author = {Imran Anwar and Zunaira Kosar and Shaheen Nazir},
  journal= {arXiv preprint arXiv:1705.09537},
  year   = {2017}
}