The cardinality of some symmetric differences

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

doi:10.1090/S0002-9939-09-10189-2

The cardinality of some symmetric differences

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	787-797
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-09-10189-2
Publication status	Published - 2010 Mar

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "The cardinality of some symmetric differences",

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.",

author = "Huang, {Po Yi} and Ke, {Wen Fong} and Pilz, {G{\"u}nter F.}",

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AB - 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.

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JO - Proceedings of the American Mathematical Society

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ER -

The cardinality of some symmetric differences

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