The cardinality of some symmetric differences

Po Yi Huang, Wen Fong Ke, Günter F. Pilz

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Abstract

In this paper, we prove that for positive integers k and n, the cardinality of the symmetric differences of {1, 2,. . ., k}, {2, 4,. . ., 2k}, {3, 6,. . ., 3k},. . ., {n, 2n,. . ., kn} is at least k or n, whichever is larger. This solved a problem raised by Pilz in which binary composition codes were studied.

Original languageEnglish
Pages (from-to)787-797
Number of pages11
JournalProceedings of the American Mathematical Society
Volume138
Issue number3
DOIs
Publication statusPublished - 2010 Mar 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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