Quasi-linear Quotients and Shellability of Pure Simplicial Complexes |
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Authors: | Imran Anwar Zahid Raza |
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Affiliation: | 1. COMSATS , Institute of Information Technology , Lahore , Pakistan iimrananwar@gmail.com;3. National University of Computer and Emerging Sciences , Lahore , Pakistan |
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Abstract: | For a square-free monomial ideal I ? S = k[x 1, x 2,…, x n ], we introduce the notion of quasi-linear quotients. By using the quasi-linear quotients, we give a new algebraic criterion for the shellability of a pure simplicial complex Δ over [n]. Also, we provide a new criterion for the Cohen–Macaulayness of the face ring of a pure simplicial complex Δ. Moreover, we show that the face ring of the spanning simplicial complex (defined in [2 Anwar , I. , Raza , Z. , Kashif , A. Spanning simplicial complexes of uni-cyclic graphs . To appear in Algebra Colloquium . [Google Scholar]]) of an r-cyclic graph is Cohen–Macaulay. |
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Keywords: | Colon ideal Face ring of a simplicial complex Facet ideal Pure square-free monomial ideal Shellable simplicial complex |
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