THE LINEAR DISCREPANCY OF 3 × 3 × 3
1
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
3×3×3 is the meaningful smallest product of three chains of each size 2n+1 since 1×1×1 is a 1-element poset. The linear discrepancy of the product of three chains 2n×2n×2n is found as 6n3−2n2−1. But the case of the product of three chains (2n + 1)×(2n + 1)×(2n + 1) is not known yet. In this paper, we determine ld(3 × 3 × 3) as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.
Abstract
3×3×3 is the meaningful smallest product of three chains of each size 2n+1 since 1×1×1 is a 1-element poset. The linear discrepancy of the product of three chains 2n×2n×2n is found as 6n3−2n2−1. But the case of the product of three chains (2n + 1)×(2n + 1)×(2n + 1) is not known yet. In this paper, we determine ld(3 × 3 × 3) as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.
참고문헌 (5)
- G. -B. Chae, "Irreducible posets of linear discrepancy 1 and 2", FJMS, 22(2), pp.217~226 (2006)
- M. Cheong, "The linear discrepancy of the product of three chains of size 2n", FJMS, 30, pp.285~298 (2008)
- S. P. Hong, "Linear discrepancy of the product of two chains", Order, 22, pp.63~72 (2005)
- P. Fishburn, "Linear discrepancy and bandwidth", Order, 18, pp.237~245 (2001)
- P. Tanenbaum, "Linear discrepancy and weak discrepancy of partially ordered sets", Order, 18, pp.201~225 (2001)