Bull. Korean Math. Soc. 2018; 55(3): 777-788
Online first article March 8, 2018 Printed May 31, 2018
https://doi.org/10.4134/BKMS.b170236
Copyright © The Korean Mathematical Society.
Gab-Byung Chae, Minseok Cheong, Sang-Mok Kim
Wonkwang University, Korea University, Kwangwoon University
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.
Keywords: poset, linear discrepancy, ld-irreducible poset, simple poset
MSC numbers: 06A07
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