Department of Mathematics
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Item Classifications of Determinantal Varieties(Library Information Services, COMSATS University, Lahore Campus, 2019) Sana Zahoor; , FA17-RMT-054; Dr. Imran Ahmed; LHR TP 5675Let Mns be a space of matrices of order n×s with complex enteries. The determinantal singularities are defined by vanishing of all the minors of a certain size of an n ×s matrix α : Ck → Mns. The class of determinantal singularities is a more general class than the class of complete intersection singularities. The G-finite deteminacy gives a special class of determinantal varieties known as essentially isolated determinantal singularities (EIDS), firstly introduced by Ebeling and Gusein-Zade in 2009. We give a computational method to find linear forms of EIDS by programming in CItem Characterization of Line Total Simplicial Complexes(Library Information Services, COMSATS University, Lahore Campus, 2018) AYESHA ANDALIB KIRAN,; FA16-RMT-033; Dr. Imran Ahmed; LHR TP 5196In 2017, Ahmed and Mahmood introduced the line simplicial complex ∆L(G) associated to a simple graph G. The pth Betti number is the rank of the pth homology group of a topological space and it refers to the number of n-dimensional holes on a topological surface. In Theorem 3.0.15, we give formula for Betti numbers of the line simplicial complex ∆L(Wn+1) associ ated to wheel graph Wn+1 by writing code in MATLAB. We define first the line total simplicial complex ∆T(G) associated to a sim ple graph G. In Theorem 4.0.24, we prove that the line total simplicial complex ∆T(G) is connected iff G is connected. In Lemma 4.0.19, we find f-vector of the line total simplicial complex ∆T(F2n+1) associated to friend ship graph F2n+1. In Theorem 4.0.20, we give formula for Betti numbers of ∆T(F2n+1) by coding in MATLAB