The cardinality of some symmetric differences

Günter Pilz; Po-Yi Huang; Wenfong Ke

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

The cardinality of some symmetric differences

Günter Pilz
, Po-Yi Huang
, Wenfong Ke

Institute for Algebra

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

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}, ... {n,2n,...kn} is at least k or n, whatever is larger. This has applications to combinatorics and to the study of linear codes.

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 - Mar 2010

Fields of science

101001 Algebra

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10.1090/S0002-9939-09-10189-2

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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\}, ... \{n,2n,...kn\} is at least k or n, whatever is larger. This has applications to combinatorics and to the study of linear codes.",

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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}, ... {n,2n,...kn} is at least k or n, whatever is larger. This has applications to combinatorics and to the study of linear codes.

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JO - Proceedings of the American Mathematical Society

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The cardinality of some symmetric differences

Abstract

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