THE NUMBER OF NON-POSET MATRICES
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Any labelled n-poset can be written in terms of matrix representation. This matrix is called the labelled matrix of a labelled n- poset. In point of view of graph theory, the labelled matrix of a labelled n-poset is the adjacency matrix of the comparability graph of a labelled n-poset. There are matrices which are not adjacency matrices of the comparability graphs of a labelled n-poset, say non-poset matrices of order n. In this paper, the number of non-poset matrices which are not adjacency matrices of the comparability graphs of the labelled n-posets of linear discrepancy two is obtained by using a method of the partitions of a number.
Abstract
Any labelled n-poset can be written in terms of matrix representation. This matrix is called the labelled matrix of a labelled n- poset. In point of view of graph theory, the labelled matrix of a labelled n-poset is the adjacency matrix of the comparability graph of a labelled n-poset. There are matrices which are not adjacency matrices of the comparability graphs of a labelled n-poset, say non-poset matrices of order n. In this paper, the number of non-poset matrices which are not adjacency matrices of the comparability graphs of the labelled n-posets of linear discrepancy two is obtained by using a method of the partitions of a number.
참고문헌 (5)
- M. Cheong, "Enumeration of Labelled n-posets of linear discrepancy two"
- S. P. Gudder, "Probabilities of Consecutive Integers in Lotto", Math-ematics Magazine, 74(3), pp.216~222 (2001)
- 정민석, "Simple posets with respect to linear Discrepancies", Advanced Studies in Contemporary Mathematics, 23(1), pp.171~180 (2013), 장전수학회
- 김상목, "A NOTE ON ISOTONE MATRIX AND LINEAR DISCREPANCY", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 12(1), pp.31~36 (2009), 장전수학회
- J. Negger, "Basic posets" (1998), World Scientific