THE LINEAR DISCREPANCY OF 3 × 3 × 3

- Journal title : Communications of the Korean Mathematical Society
- Volume 25, Issue 1, 2010, pp.19-25
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2010.25.1.019

Title & Authors

THE LINEAR DISCREPANCY OF 3 × 3 × 3

Chae, Gab-Byoung; Cheong, Min-Seok; Kim, Sang-Mok;

Chae, Gab-Byoung; Cheong, Min-Seok; Kim, Sang-Mok;

Abstract

is the meaningful smallest product of three chains of each size 2n+1 since is a 1-element poset. The linear discrepancy of the product of three chains is found as . But the case of the product of three chains is not known yet. In this paper, we determine ld as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.

Keywords

poset;linear discrepancy;

Language

English

References

1.

G. -B. Chae, M. Cheong, and S. -M. Kim, Irreducible posets of linear discrepancy 1 and 2, FJMS 22 (2006), no. 2, 217–226.

2.

M. Cheong and S.-M. Kim, The linear discrepancy of the product of three chains of size 2n, FJMS 30 (2008), 285–298.

3.

S. P. Hong, J. Y. Hynn, H. K. Kim, and S.-M. Kim, Linear discrepancy of the product of two chains, Order 22 (2005), 63–72.