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THE LINEAR DISCREPANCY OF A PRODUCT OF TWO POSETS
- Authors
- Cheong, Minseok
- Issue Date
- 2017
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- poset; product of posets; linear discrepancy
- Citation
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.54, no.3, pp.1081 - 1094
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 54
- Number
- 3
- Start Page
- 1081
- End Page
- 1094
- ISSN
- 1015-8634
- Abstract
- For a poset P = (X, <= p), the linear discrepancy of P is the minimum value of maximal differences of all incomparable elements for all possible labelings. In this paper, we find a lower bound and an upper bound of the linear discrepancy of a product of two posets. In order to give a lower bound, we use the known result, ld(m x n) = [mm/2] - 2. Next, we use Dilworth's chain decomposition to obtain an upper bound of the linear discrepancy of a product of a poset and a chain. Finally, we give an example touching this upper bound.
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