• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.189-196
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• 2021

Using ld-irreducible posets, we can easily characterize posets with respect to linear discrepancy. However, it is difficult to have the list of all the irreducible posets with respect to a given linear discrepancy. In this paper, we investigate some properties of disconnected posets and connected posets with respect to linear discrepancy, respectively and then we find various relationships between ld-irreducibily and connectedness. From these results, we suggest some methods to construct ld-irreducible posets.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.777-788
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• 2018

A simple poset is a poset whose linear discrepancy increases if any relation of the poset is removed. In this paper, we investigate more important properties of simple posets such as its width and height which help to construct concrete simple poset of linear discrepancy l. The simplicity of a poset is similar to the ld-irreducibility of a poset. Hence, we investigate which posets are both simple and ld-irreducible. Using these properties, we characterize n-posets of linear discrepancy n - k for k = 2, 3, and, lastly, we also characterize a poset of linear discrepancy 3 with simple posets and ld-irreducible posets.