Les hiérarchies de parties et leur demi-treillis

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1. Bandelt H.J., Barthelemy J.P., "Medians in median graphs", Discrete Applied Math., 8 (1984), 131-142. Zbl0536.05057MR743019
2. Bandelt H.J., Hedlikova J., "Median Algebras", Discrete Math., 45 (1983), 1-30. Zbl0506.06005MR700848
3. Barbut M., "Mediane, distributivité, éloignements" (1961), Math. Sci. hum., 70 (1980), 5-31. Zbl0439.06007MR593433
4. Barbut M., Monjardet B., Ordre et classification. Algèbre et Combinatoire, Paris, Hachette, 1970. Zbl0267.06001
5. Barthelemy J.P., "Remarques sur les propriétés métriques des ensembles ordonnés", Math. Sci. hum., 61 (1978), 39-60. Zbl0419.06001MR508761
6. Barthelemy J.P., "Caractérisations axiomatiques de la distance de la différence symétrique entre les relations binaires", Math. Sci. hum., 67 (1979), 85-113. Zbl0418.06003
7. Barthelemy J.P., Leclerc B., Monjardet B., "Quelques aspects du consensus en classification", in : DIDAY E., et al., eds, Data Analysis and Informatics 3, Amsterdam, North-Holland, 1984a, 307-316. Zbl0566.62047MR787643
8. Barthelemy J.P., Leclerc B., Monjardet B., "Ensembles ordonnés et taxonomie mathématique", in : POUZET M., RICHARD D., eds, Orders : description and roles, Amsterdam, North-Holland, 1984b, 523-548. Zbl0566.62051MR779868
9. Benzecri J.P., "Description mathématique des classifications"(1967), in : L'analyse des données I, La Taxinomie, Paris, Dunod, 1973. MR593138
10. Berge C., Graphes et hypergraphes, Paris, Dunod, 1970. Graphs and hypergraphs, Amsterdam, North-Holland, 1973. Zbl0213.25702MR357171
11. Boorman S.A., Olivier D.C., "Metrics on spaces of finite trees", J. Math. Psychol., 10 (1973), 26-59. Zbl0271.92011MR317975
12. Brown E.K., Day W.H.E., "A computationally Efficient Approximation to the Nearest Neighbour Interchange Metric", J. of Classification1 (1984), 93-124. Zbl0563.62033MR800508
13. Cayley A., "On the theory of the analytic forms called trees", Phil. Magazine, XIII, (1857), 172-176. Collected mathematical papers, vol.3, p.242, Cambridge University Press. 
14. Chandon J.L., Pinson S., Analyse typologique, Paris, Masson, 1980. Zbl0505.62039MR619538
15. Comtet L., Analyse combinatoire, Paris, Presses Universitaires de France, 1970a. Advanced Combinatorics, Dordrecht, Reidel, 1974. 
16. Comtet L., "Sur le quatrième problème et les nombres de Schröder", C.R. Acad. Sci.ParisA-271 (1970 b) 913-916. Zbl0207.02503MR272648
17. Comyn G., Van Dorpe J.C., "Valuation et semi-modularité dans les demi-treillis", Math. Sci. hum., 56 (1976), 63-75. Zbl0367.06009MR444542
18. Dobson A.J., "Unrooted trees for numerical taxonomy", J. Appl. Prob., 11 (1974), 32-42. Zbl0277.92004MR357179
19. Etherington I.M.H., "On non-associative combinations", Proc. Roy. Soc. Edinburgh, 59 (1939), 153-162. Zbl0021.29404JFM65.1138.06
20. Flament C., Leclerc B., "Arbres minimaux d'un graphe préordonné", Discrete Math., 46 (1983), 159-171. Zbl0518.05024MR710887
21. Foulds L.R., Robinson R.W., "Determining the asymptotic number of phylogenetic trees", in : Combinatorial Mathematics VII, Lecture Notes in Mathematics829, Berlin, Springer-Verlag, 1980. Zbl0444.05046MR611187
22. Foulds L.R., Robinson R.W., "Enumeration of binary phylogenetic trees", in : Combinatorical Mathematics VIII, Lecture Notes in Mathematics884, Berlin, Springer-Verlag, 1982. Zbl0469.05038
23. Gardner M., "Mathematical games : Catalan numbers", Scientific American235, (June 1976), 120-125. 
24. Gould H., "Research bibliography of two special numbers sequences", Mathematica Monongaliae, 12 (1971). Zbl0226.10002MR279029
25. Guilbaud G.Th., "Un problème leibnitzien : les partages en nombres entiers", Math. Sci. hum., 17 (1968), 13-36. MR211937
26. Guilbaud G.Th., Rosenstiehl P., "Analyse algébrique d'un scrutin", Math. Sci. hum., 4 (1960), 9-33. 
27. Harary F., Graph Theory, Reading, Mass., Addison-Wesley, 1969. Zbl0182.57702MR256911
28. Harary F., Mowshowitz A., Riordan J., "Labelled trees with unlabelled endpoints", J. Comb. Theory, 6 (1969), 60-64. Zbl0175.50105MR236055
29. Harding E.S., "The probabilities of rooted tree-shapes generated by random bifurcations", Adv. Appl. Prob., 3 (1971), 44-77. Zbl0241.92012MR282451
30. Hartigan J.A., Clustering algorithms, New-York, Wiley, 1975. Zbl0372.62040MR405726
31. Haskins L., Gudder S., "Height on posets and graphs", Discrete Math., 2, (1972), 357-382. Zbl0238.06002MR306059
32. Jarvis J.P., Luedeman J.K., Shier D.R., "Counterexamples in Measuring the distance between binary trees", Mathematical Social Sciences, 4 (1983), 271-274. Zbl0517.05027
33. Knuth D.E., The art of computer programming, vol. 1 : Fundamental algorithms, vol.3 : Sorting and searching, Reading, Mass., Addison-Wesley, 1969- 1973. MR286317
34. Leclerc B., "Description combinatoire des ultramétriques", Math. Sci. hum., 73 (1981), 5-37. Zbl0476.05079MR623034
35. Leclerc B., Description, évaluation et comparaison des hiérarchies de parties, rapport CAMS-EHESS, 1982. 
36. Lerman I.C., Les bases de la classification mathématique, Paris, Gauthier-Villars, 1970. Zbl0199.51402MR349079
37. Lerman I.C., Classification et analyse ordinale des données, Paris, Dunod, 1981. Zbl0485.62051MR645150
38. Margush T., M F.R., "Consensus n-trees", Bull. Math. Biology, 43 (1981), 239-244. Zbl0455.92019MR661505
39. Monjardet B., "Caractérisations métriques des ensembles ordonnés semimodulaires", Math. Sci. hum., 56 (1976), 77-87. Zbl0367.06010MR444543
40. Monjardet B., "Metrics on a partially ordered set. A survey", Discrete Math., 35 (1981), 173-181. Zbl0463.46016MR620670
41. Moon J.W., "Enumerating labelled trees", in : HARARY F., ed., Graph Theory and Theoretical Physics, London, Academic Press, 1967. Zbl0204.24502MR231755
42. Moore G.W., Goodman M., Barnabas J., "An iterative approach from the stand-point of the additive hypothesis to the dendrogram problem posed by molecular data sets", J. Theor. Biol., 38 (1973), 423-457. 
43. Murtagh F., "Counting dendrograms : a survey", Discrete Applied Math., 7 (1984), 191-199. Zbl0528.62055MR727923
44. Ore O., "Chains in partially ordered sets", Bull. Amer. Math. Soc., 49 (1943), 558-566. Zbl0060.06104MR9017
45. Otter R., "The number of trees", Ann. Math., 49, n°3 (1948), 583-599. Zbl0032.12601MR25715
46. Robinson D.F., "Comparison of Labeled Trees with valency three", J. of Comb. Theory11 (1971), 105-119. Zbl0185.27704MR294170
47. Rosenstiehl P., "L'arbre minimum d'un graphe", in : ROSENSTIEHL P., ed., Théorie des graphes (Rome, 1966), Paris, Dunod, 1967. Zbl0202.55902
48. Schader M., "Hierarchical analysis : classification with ordinal object dissimilarities", Metrika, 27 (1980), 127-132. Zbl0438.62046MR577564
49. Schader M., Scharfe und unscharfe Klassifikation Qualitativer Daten, Mathematic Systems in Economics65, Verlagsgruppe Athenanüm, 1981. Zbl0511.62062MR638037
50. Sholander M., "Medians, Lattices and Trees", Proc. Amer. Math. Soc., 5 (1954), 808-812. Zbl0056.26201MR64750
51. Schröder E., "Vier combinatorische probleme", S. fur Mat. Phys., 15 (1870), 361-376. JFM02.0108.04
52. Sloane N.J.A., A handbook of integer sequences, New-York, Academic Press, 1973. Zbl0286.10001MR357292
53. Waterman M.S., Smith T.F., "On the similarity of dendrograms", J. Theor. Biol.73 (1978), 789-800. MR496831
54. Wedderburn J.H., "The functional equation g(x2) = 2x + [g(x)]2", Ann. Math., 24 (1922), 121-140. MR1502633JFM49.0244.02

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