Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE LINEAR DISCREPANCY OF A PRODUCT OF TWO POSETS

  • Cheong, Minseok (Information Security Convergence College of Informatics Korea University)
  • Received : 2016.06.13
  • Published : 2017.05.31
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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.

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References

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