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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Universal cycles for minimum coverings of pairs by triples, with application to 2-radius sequences
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by Yeow Meng Chee, San Ling, Yin Tan and Xiande Zhang PDF
Math. Comp. 81 (2012), 585-603 Request permission

Abstract:

A new ordering, extending the notion of universal cycles of Chung et al. (1992), is proposed for the blocks of $k$-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established for all orders. The application to the construction of short 2-radius sequences is given, along with some new 2-radius sequences found through a computer search.
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Additional Information
  • Yeow Meng Chee
  • Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
  • Email: ymchee@ntu.edu.sg
  • San Ling
  • Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
  • Email: lingsan@ntu.edu.sg
  • Yin Tan
  • Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
  • Email: tanyin@ntu.edu.sg
  • Xiande Zhang
  • Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
  • Email: ziandezhang@ntu.edu.sg
  • Received by editor(s): September 20, 2009
  • Received by editor(s) in revised form: August 6, 2010
  • Published electronically: June 21, 2011
  • Additional Notes: This research was supported in part by the National Research Foundation of Singapore under Research Grant NRF-CRP2-2007-03 and by the Nanyang Technological University under Research Grant M58110040.
  • © Copyright 2011 American Mathematical Society
  • Journal: Math. Comp. 81 (2012), 585-603
  • MSC (2010): Primary 05B05, 05B07, 05B40; Secondary 05C38, 68R05
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02473-7
  • MathSciNet review: 2833510