Thin Lehman matrices arising from finite groups
| Autor: | Hidehiro Shinohara |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
Finite group Numerical Analysis Algebra and Number Theory Thin Lehman matrix Identity matrix Combinatorics Integer matrix Matrix (mathematics) Minimally nonideal matrix Discrete Mathematics and Combinatorics Matrix analysis Nonnegative matrix Geometry and Topology Near-factorization 1-Overlapped factorization Mathematics |
| Zdroj: | Linear Algebra and its Applications. 436(4):850-857 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2011.02.047 |
| Popis: | Two n × n ( 0 , 1 ) matrices X , Y are called thin Lehman matrices if they are solutions of the matrix equation XY T = J n + I n , where J n is the n × n matrix of all 1 s and I n is the identity matrix. These matrices are important in the set covering problem, but few examples are known. In this paper, we will introduce the notion of 1 -overlapped factorizations of finite groups which constructs a new class of thin Lehman matrices. Moreover, we will study some structural properties of 1 -overlapped factorizations. |
| Databáze: | OpenAIRE |
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