Uniformly increasing Hypergraphs: On the regularity of Inclusion Ideals associated to Uniformly increasing Hypergraphs

Anwar, Imran, Inam, Amina

ISBN 10: 3846534218 / ISBN 13: 9783846534212

Published by LAP LAMBERT Academic Publishing, 2011

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Bibliographic Details

• Title: Uniformly increasing Hypergraphs: On the regularity of Inclusion Ideals associated to Uniformly increasing Hypergraphs
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2011
• Language: English
• ISBN 10: 3846534218
• ISBN 13: 9783846534212
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

The aim of this book is to give a description on the algebra associating to hypergraph, which is the generalized form of simple graphs and simplicial complexes. Algebraic study of combinatorial objects has been widely studied by different algebraist. Our main work in this regard is to associate an algebra to a special class of hypergraphs namely uniformly increasing hypergraphs H(X, E, d). This class of hypergraphs is important in one sense that they can neither be treated as simple graphs nor simplicial complexes. So, this work is the first stepping towards exploring the algebra associated to uniformly increasing hypergraphs H(X, E, d). In this book, we introduce inclusion ideals I(H) associated to the uniformly increasing hypergraphs H(X, E, d). We discuss some algebraic properties of the inclusion ideals. In particular, we give an upper bound of the Castlenouvo-Mumford regularity of the special dual ideal.

About the Author

Dr. Imran Anwar:He is working as an Asst. Professor in the department of Mathematics COMSATS Institute of Information Technology, Lahore-Pakistan. His area of interest is combinatorial aspects of Commutative Algebra.Amina Inam:She has done her MS thesis under the supervision of Dr. Imran Anwar on the uniformly increasing hypergraphs.