[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b160501

THE LINEAR DISCREPANCY OF A PRODUCT OF TWO POSETS

Cheong, Minseok (Information Security Convergence College of Informatics Korea University)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 1081-1094 More about this Journal

Abstract

For a poset $P=(X,{\leq}_P)$ , 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, $ld({\mathbf{m}}{\times}{\mathbf{n}})={\lceil}{\frac{mn}{2}}{\rceil}-2$ . 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.

Keywords

poset; product of posets; linear discrepancy;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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