Document Zbl 0472.06007

On the Ferrers dimension of a digraph. (English) Zbl 0472.06007

Discrete Math. 38, 47-52 (1982).

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MSC:

06A06	Partial orders, general
05A15	Exact enumeration problems, generating functions
05C20	Directed graphs (digraphs), tournaments

Keywords:

number of linear orders; Ferrer’s digraphs; Ferrer’s dimension; order dimension of posets

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References:

[1]	Bouchet, A., Etude combinatoire des ordonnés finis, (Applications. Applications, Thèse de Doctorat d’Etat (1971), Université Scientifique et Médicale de Grenoble)
[2]	Chvátal, V.; Hammer, P. L., Aggregation of inequalities in integer programming, Ann. Discrete Math., 1, 145-162 (1977) · Zbl 0384.90091
[3]	Cogis, O., Détermination d’un préordre total contenant un préordre et contenu dans une relation de Ferrers, lorsque leur domaine commun est fini, C.R. Acad. Sci. Paris, 283A, 1007-1009 (1976) · Zbl 0363.04004
[4]	Cogis, O., Ferrers digraphs and threshold graphs, Discrete Math., 38, 33-46 (1982), in this issue · Zbl 0472.06006
[5]	Cogis, O., On a digraph dimension, Ann. Discrete Math., 8, 279-281 (1980) · Zbl 0447.05028
[6]	Cogis, O., Dimension Ferrers des graphes orientés, (Thése de Doctorat d’Etat (1980), Université Pierre et Marie Curie: Université Pierre et Marie Curie Paris) · Zbl 0421.05031
[7]	Dushnick, B.; Miller, E. W., Partially ordered sets, Amer. J. Math., 63, 600-610 (1941) · Zbl 0025.31002
[8]	Horowitz, E.; Sahni, S., Fundamentals of Computers Algorithms (1978), Pitman: Pitman London · Zbl 0442.68022
[9]	Karp, R. M., Reducibility among combinatorial problems, (Miller, R. E.; Thatcher, J. W., Complexity of Computers Computations (1972), Plenum Press: Plenum Press New York), 85-104 · Zbl 0366.68041
[10]	Monjardet, B., Axiomatiques et propriétés des quasi-ordres, Math. Sci. Humaines, 63, 51-82 (1978) · Zbl 0417.06005
[11]	Ore, O., Theory of graphs, Amer. Math. Soc. Coll. Publ., 38 (1962) · Zbl 0105.35401
[12]	Riquet, J., Les relations de Ferrers, C.R. Acad. Sci. Paris, 232, 1729-1730 (1951) · Zbl 0042.24317

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