Zero-Sum Flows in Designs and Hypergraphs

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Bahmani, Asghar | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43566 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saieed
Abstract:
Let X = fx1; : : : ; xng be the set of vertices of a hypergraph H and E = fe1; : : : ; emg be the set of its edges. The incidence matrix of hypergraph H is an n m and (0; 1)-matrix, N, such that nij = 1 if xi 2 ej and nij = 0, otherwise. A zero-sum flow for H is a vector with non-zero entries that is in the null space of N. A zero-sum k-flow is a flow with non-zero integer entries that absolue value of each entry is at
most k 1. In this thesis we study the existence of zero-sum flows for designs and hypergraphs. Also we consider zero-sum 3-flows in 2-Steiner designs
Keywords:
Zero-sum Flow ; Block Design ; Hypergraph

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