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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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참고문헌 (6)
참고문헌 신청
G.-B. Chae / 2006 / Irreducible posets of linear discrepancy 1 and 2 / Far East J. Math. Sci. (FJMS) 22(2):217~226
정민석 / 2013 / Simple posets with respect to linear Discrepancies / Advanced Studies in Contemporary Mathematics 23(1):171~180
D. M. Howard / 2008 / Irreducible width 2 posets of linear discrepancy 3 / Order 25(2):105~119
D. M. Howard / 2007 / A characterization of partially ordered sets with linear discrepancy equal to 2 / Order 24(3):139~153
S.-L. Ng / 2004 / A characterisation of posets that are nearly antichains / Order 21(1):1~5
정민석 / 2013 / Simple posets with respect to linear Discrepancies / Advanced Studies in Contemporary Mathematics 23(1):171~180
D. M. Howard / 2008 / Irreducible width 2 posets of linear discrepancy 3 / Order 25(2):105~119
D. M. Howard / 2007 / A characterization of partially ordered sets with linear discrepancy equal to 2 / Order 24(3):139~153
S.-L. Ng / 2004 / A characterisation of posets that are nearly antichains / Order 21(1):1~5
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