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.
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.
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