ENUMERATION OF OPTIMALLY LABELLED n-POSETS OF LINEAR DISCREPANCY TWO
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Any labelled n-poset of linear discrepancy two can be writ- ten in terms of matrix representations. But there are matrices which are not the adjacency matrices of the comparability graphs of any poset at all, say non-poset matrices of order n, and matrices which are of tight- ness two but of linear discrepancy one, say non-optimal labelled matrices of order n in matrix representations. In this paper, the number of opti- mally labelled n-posets of linear discrepancy two is obtained by count- ing the number of non-poset matrices and the number of non-optimal labelled matrices.
Abstract
Any labelled n-poset of linear discrepancy two can be writ- ten in terms of matrix representations. But there are matrices which are not the adjacency matrices of the comparability graphs of any poset at all, say non-poset matrices of order n, and matrices which are of tight- ness two but of linear discrepancy one, say non-optimal labelled matrices of order n in matrix representations. In this paper, the number of opti- mally labelled n-posets of linear discrepancy two is obtained by count- ing the number of non-poset matrices and the number of non-optimal labelled matrices.
참고문헌 (8)
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