Simple posets with respect to linear Discrepancies
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In this paper, we give a characterization of n-posets with respect to linear discrepancy. We rst obtain the uniquely dened tri-angular matrix r lled with 1 from the interchanging operation on the matrix representation of naturally labeled posets and their linear dis-crepancies. Next, for each linear discrepancy l and each cardinality of poset n, we dene the (n; l)-simple poset S with the property that a removal of any order relation from S causes its linear discrepancy in-creasing. Then, in terms of poset extension of (n; l)-simple posets, we give a characterization of n-posets with respect to linear discrepancy l, by using the fact that (n; l)-simple posets are represented as rs. Lastly, as an application of simple posets represented by rs, we count all n-posets of linear discrepancy 1, which is identical to the previous result due to Tanenbaum, et al. [Linear discrepancy and weak discrepancy of partially ordered sets, Order 18 (2001), 201-225].
Abstract
In this paper, we give a characterization of n-posets with respect to linear discrepancy. We rst obtain the uniquely dened tri-angular matrix r lled with 1 from the interchanging operation on the matrix representation of naturally labeled posets and their linear dis-crepancies. Next, for each linear discrepancy l and each cardinality of poset n, we dene the (n; l)-simple poset S with the property that a removal of any order relation from S causes its linear discrepancy in-creasing. Then, in terms of poset extension of (n; l)-simple posets, we give a characterization of n-posets with respect to linear discrepancy l, by using the fact that (n; l)-simple posets are represented as rs. Lastly, as an application of simple posets represented by rs, we count all n-posets of linear discrepancy 1, which is identical to the previous result due to Tanenbaum, et al. [Linear discrepancy and weak discrepancy of partially ordered sets, Order 18 (2001), 201-225].
참고문헌 (12)
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