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Graphs and Combinatorics

, Volume 34, Issue 6, pp 1459–1467 | Cite as

One-Overlapped Factorizations of Non-abelian Groups

  • Nicola Pace
Original Paper
  • 33 Downloads

Abstract

One-overlapped factorizations of finite groups were introduced by Shinohara (Linear Algebra Appl. 436(4):850–857, 2012) for constructing a new class of thin Lehman matrices. However, all known examples and constructions arise from cyclic or dihedral groups. In this paper, we prove the existence of one-overlapped factorizations of non-abelian groups that are not dihedral and describe a simple construction. The corresponding incidence structures and Lehman matrices are also considered.

Keywords

Dihedral group General linear group Set cover problem Thin Lehman matrix 

Mathematics Subject Classification

05B20 20D99 

Notes

Acknowledgements

This work was supported by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF). The author would like to thank Dr. Marco A. Pellegrini for his comments on the previous version of this paper.

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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Operations ResearchTechnical University of MunichMunichGermany

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