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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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