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THE LINEAR DISCREPANCY OF 3 × 3 × 3

  • Chae, Gab-Byoung (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Cheong, Min-Seok (Division of Mathematics, Sogang University) ;
  • Kim, Sang-Mok (Division of general education-Mathematics, Kwangwoon University)
  • Published : 2010.01.31

Abstract

$3{\times}3{\times}3$ is the meaningful smallest product of three chains of each size 2n+1 since $1{\times}1{\times}1$ is a 1-element poset. The linear discrepancy of the product of three chains $2n{\times}2n{\times}2n$ is found as $6n^3-2n^2-1$. But the case of the product of three chains $(2n + 1){\times}(2n + 1){\times}(2n + 1)$ is not known yet. In this paper, we determine ld$(3{\times}3{\times}3)$ as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.

Keywords

poset;linear discrepancy

References

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