Description combinatoire des ultramétriques
Leclerc, Bruno
Mathématiques et Sciences humaines, Tome 76 (1981), p. 5-37 / Harvested from Numdam
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@article{MSH_1981__73__5_0,
     author = {Leclerc, Bruno},
     title = {Description combinatoire des ultram\'etriques},
     journal = {Math\'ematiques et Sciences humaines},
     volume = {76},
     year = {1981},
     pages = {5-37},
     mrnumber = {623034},
     zbl = {0476.05079},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/MSH_1981__73__5_0}
}

Leclerc, Bruno. Description combinatoire des ultramétriques. Mathématiques et Sciences humaines, Tome 76 (1981) pp. 5-37. http://gdmltest.u-ga.fr/item/MSH_1981__73__5_0/

[1] Barbut M., Monjardet B., Ordre et classification, algèbre et combinatoire, tomes 1 et 2, Paris, Hachette, 1970. | Zbl 0267.06001

[1a] Barbut M., "Médianes, distributivité, éloignements", Math. Sci. hum.70 (1980), 5-32. | Numdam | MR 593433

[2] Barthelemy J.P., Propriétés métriques des ensembles ordonnés. Comparaison et agrégation des relations binaires, thèse, Faculté des Sciences et des Techniques de l'Université de Franche-Comté, Besançon, 1979.

[2a] Barthelemy J.P., Monjardet B., "The median procedure in cluster analysis and social choice theory", Mathematical Social Sciences, à paraître en 1981. | MR 616379 | Zbl 0486.62057

[3] Benzecri J.P., "Description mathématique des classifications ", in : L'analyse des données. I. La taxonomie, Paris, Dunod, 1973.

[4] Berge C., Graphes et hypergraphes, Paris, Dunod, 1970. Trad. en anglais : Graphs and Hypergraphs, Amsterdam, North Holland, 1973. | MR 357173 | Zbl 0213.25702

[5] Birkhoff G., Lattice theory, American Mathematical Society Colloquium Publications XXV, Providence, American Mathematical Society, 1967. | MR 227053 | Zbl 0153.02501

[6] Boorman S.A., Olivier D.C., "Metrics on spaces of finite trees", J. Math. Psychol. 10 (1973), 26-59. | MR 317975 | Zbl 0271.92011

[7] Buneman P., "Filiation of manuscripts",in : Hodson F.R., Kendall D.G., Tautu P., eds., Mathematics in the Archaeological and Historical Sciences, Edinburgh, Edinburgh University Press, 1971.

[8] Caillez F., Pages J.P., Introduction à l'analyse des données, Paris, SMASH, 1976.

[9] Chandon J.L., Lemaire J., Pouget J., "Construction de l'ultramétrique la plus proche d'une dissimilarité au sens des moindres carrés", RAIRO 14 (mai 1980), n°2, 157-170. | Numdam | MR 575663 | Zbl 0434.90051

[10] Choquet G., "Etude de certains réseaux de routes", C.R. Acad. Sci. Paris 206 (1938), 310. | JFM 64.0707.02 | Zbl 0018.17603

[10a]Defays D., "Relations floues et analyse hiérarchique de questionnaires", Math. Sci. hum. 55 (1976), 45-60. | Numdam | MR 444294

[11] Dijkstra E., "Two problems in connections with graphs ", Num. Math. 1 (1959), 269-271. | MR 107609 | Zbl 0092.16002

[12] Dubreil-Jacotin M.L., Lesieur L., Croisot R., Leçons sur la théorie des treillis. Cahiers Scientifiques 21, Paris, Gauthier-Villlars, 1953. | Zbl 0051.26005

[13] Dunn J.C., "A graph theoretic analysis of pattern classification via Tamura's fuzzy relations", IEEE Trans. Syst. Man. Cybern. SCM-4 (May 74), n°3, 61-66. | Zbl 0297.68077

[14] Edmunds J., Fulkerson D.R., "Bottleneck extrema", J. Comb. Theory 8 (1970), 299-306. | MR 255235 | Zbl 0218.05006

[15] Flament C., "Equilibre d'un graphe, quelques résultats algébriques", Math. Sci. hum. 30 (1970), 5-22. | Numdam | MR 278978 | Zbl 0222.05124

[16] Flament C., "Arêtes maximales des cocycles d'un graphe préordonné", Math. Sci. hum. 51 (1975), 5-12. | Numdam | MR 476572 | Zbl 0332.05102

[17] Flament C., "Un modèle des jugements de similitude", Math. Sci. hum. 65 (1979), 5-21. | Numdam | MR 539410 | Zbl 0462.92018

[18] Florek K., Lukaszewicz J., Perkal H., Steinhaus H., Zubrzycki S., "Sur la liaison et la division des points d'un ensemble fini", Colloquium Mathematicum 2 (1951), 282-285. | MR 48832 | Zbl 0045.26103

[19] Ford L.R.,Jr, Fulkerson D.R., Flows- in networks, Santa Monica, The Rand Corporation, 1962. Trad. Française : Flots dans les graphes, Paris, Gauthier-Villars, 1967. | MR 159700

[20] Fulkerson D.R., "Flows networks and combinatorial operations research", Am. Math. Monthly 73 (1966), n°2. Repris légèrement modifié dans : Fulkerson D.R., Studies in Graph Theory, The mathematical Association of America, 1975. | MR 395761 | Zbl 0168.40706

[21] Ghouila-Houri A., Flots et tensions dans un graphe, thèse, Paris, Gauthier-Villars, 1964. | MR 182575

[22] Gomory R.E., Hu T.C., "Multi-terminal network flows", J. of SIAM 9 (1961), n°4, 551-570. Repris : Multi-terminal flows in a network, in : FULKERSON D.R., ed., Studies in Graph Theory, The mathematical Association of America, 1975. | MR 135624 | Zbl 0112.12405

[23] Gondran M., "Valeurs propres et vecteurs propres en classification hiérarchique", R.A.I.R.O. Informatique théorique 10, n°3 (mars 1976), 39-46. Trad. en anglais :"Eigenvalues and eigenvectors in hierarchical classification" in: J.L. BARRA, et al. eds, Recent Developments in Statistics, North Holland, 1977. | Numdam | MR 411059 | Zbl 0362.62062

[24] Gondran M., Classification hiérarchique et connexité, communication aux secondes journées internationales d'analyse des données et informatique de l'IRIA (Versailles 1979).

[25] Gondran M., Minoux M., Graphes et algorithmes, Paris, Eyrolles, 1979. | MR 615739 | Zbl 0497.05023

[26] Gower J.C., Ross G.J.S., "Minimum spanning tree and single linkage cluster analysis", Applied Statistics 18 (1969), 54-64. | MR 242315

[27] Hage P., "Structural balance and clustering in bushmen kinship relations", Behavioural Science 21 (1976), 36-47.

[28] Delattre M., Hansen P., "Bicriterion cluster analysis", IEEE Trans. on pattern analysis and machines Intelligence (1980) à paraître. | Zbl 0458.62049

[29] Harary F., Graph Theory, Reading, Mass. Addison-Wesley, 1969. | MR 256911 | Zbl 0182.57702

[30] Haskins L., Gudder S., "Height on posets and graphs", Discrete Math. 2 (1972), 357-382. | MR 306059 | Zbl 0238.06002

[31] Hu T.C., "The maximum capacity route problem", Operation research 8 (1960), 733-736. | MR 128558

[32] Hubert L., "Spanning trees and aspects of clustering", British J. of Math. and Statist. Psychology 27 (1974), 14-28. | Zbl 0288.92024

[33] Hubert L., "Data analysis implications of some concepts related to the cuts of a graph", J. of Math. Psychology 15 (1977), 199-208. | MR 449791 | Zbl 0354.92047

[33a] Jacquet-Lagreze E., La modélisation des préférences, préordres, quasi-ordres et relations floues, thèse, Paris, Université René Descartes (PARIS-V), 1975.

[34] Jardine N., Sibson R., Mathematical taxonomy, New York, Wiley, 1971. | MR 441395 | Zbl 0322.62065

[35] Kalaba R., "Graph theory and automatic control", in : BECKENBACH E.F., ed. Applied combinatorial mathematics, New York, Wiley, 1964. | MR 214388 | Zbl 0143.12502

[36] Karp R.M., "Reducibility among combinatorial problems". In : MILLER R.E., THATCHER J.W., eds., Complexity of computer computations, New York, Plenum, 1972. | MR 378476

[37] Katai O., Iwai S., "Studies on the balancing, the minimal balancing and the minimal balancing process for social groups with planar and non planar structures", J. of Math. Psychology 18 (1978), 260-269. | Zbl 0394.92027

[38] Kim K.H., Roush F.W.," Ultrametrics and matrix theory", J. Math. Psychology 18 (1978), n°2. | MR 515234 | Zbl 0395.92025

[39] Kruskal J., "On the shortest spanning tree of a graph and a travelling salesman problem" , Proc. Amer. Math. Soc. 7 (1956), 48-50. | MR 78686 | Zbl 0070.18404

[40] Leclerc B., "An application of combinatorial theory to hierarchical classification " , in : BARRA J.L., et al., eds., Recent developments in statistics, North Holland, 1977. | MR 468039 | Zbl 0362.62063

[41] Leclerc B., "Matroides sur un ensemble ordonné. Bases minimales, circuits et cocircuits, parties commençantes", C.R. Acad. Sci. Paris. A-286 (février 1978), 301-304. | MR 472574 | Zbl 0381.05022

[42] Leclerc B., "Semi-modularité des treillis d'ultramétriques ", C.R. Acad. Sci. Paris A-288 (mars 1979), 575-577. | MR 531585 | Zbl 0414.06008

[43] Leclerc B., Sur le nombre d'arbres minimums d'une ultrmnétrique, note (1981).

[44] Lerman I.C., Les bases de la classification automatique, Paris, Gauthier-Villars, 1970. | MR 349079 | Zbl 0199.51402

[45] Matula D.W., "The cohesive strength of graphs" in : The many facets of Graph Theory, Berlin, Springer-Verlag, 1969. | MR 252262 | Zbl 0196.27204

[46] Matula D.W., "k-components, clusters and slicings in graphs ", SIAM J. Appl. Math. 22 (1972), 459-480. | MR 306051 | Zbl 0243.05111

[47] Polat N., Flament C., "Applications galoisiennes proches d'une application entre treillis ", Math. Sci. hum. 70 (1980), 33-49. | Numdam | MR 593434 | Zbl 0434.06006

[48] Pollack M., "The maximum capacity route through a network ", Op. research 8 (1960), 733-736. | MR 128558

[49] Prim R.C., "Shortest connection network and some generalizations ", Bell System techn. J. 36 (1957), 1389-1401.

[50] Reingold E.M., Nievergelt J., Deo N., Combinatorial algorithms, theory and practice, Englewood Cliffs (N.J.), Prentice Hall, 1977. | MR 471431 | Zbl 0367.68032

[51] Roberts F.S., Discrete mathematical models with applications to social, biological and environmental problems, Englewood Cliffs (N.J.), Prentice Hall, 1976. | Zbl 0363.90002

[52] Roberts F.S., Graph theory and its applications to problems of society, Philadelphie, Society for industrial and applied mathematics,1978. | MR 508050 | Zbl 0452.05001

[53] Rosenstiehl P., "L'arbre minimum d'un graphe",in:ROSENSTIEHL P., ed.,Théorie des graphes, Rome, 1966, Paris, Dunod, 1967. | Zbl 0202.55902

[54] Roux M.," Notes sur l'arbre de longueur minima", Rev. Statist. Appl. 23 (1975), n°2, 29-35. | Numdam | MR 463033

[55] Ruspini E.R., "A new approach to clustering", Information and Control 15 (1969), 22-32. | Zbl 0192.57101

[56] Schader M., "Hierarchical analysis : Classification with ordinal object dissimilarities", Metrika, 27 (1980), 127-132. | MR 577564 | Zbl 0438.62046

[57] Schader M., "Distance minimale entre partitions et préordonnances dans un ensemble fini", Math. Sci. hum. 67 (1979), 39-47. | Numdam | Zbl 0419.04001

[58] Sozanski T., "Processus d'équilibration et sous-graphes équilibrés d'un graphe signé complet", Math. Sci. hum. 55 (1976), 25-36. | Numdam | MR 543817

[59] Steinhaus H., Mathematical snapshots, Oxford University Press, 1960, trad. Mathématiques en instantanés, Paris, Flammarion, 1960. | MR 114721 | Zbl 0041.27502

[60] Szasz G., "Contributions to the theory of semi-modular lattices", Publ. Math. Debreczen 22 (1975) n°3-4, 205-209. | MR 412061 | Zbl 0327.06006

[61] Tamura S., Higuchi S., Tanaka K., "Pattern classification based on fuzzy relations ", IEEE Trans. on Systems, Man, and Cybernetics SCM-1 (1971), 937-944. | MR 311165 | Zbl 0224.68012

[62] Tomescu I., "Note sur une caractérisation des graphes dont le degré de déséquilibre est maximal", Math. Sci. hum. 42 (1973), 37-40. | Numdam | MR 366757 | Zbl 0266.05115

[63] Tomescu I., "Sur le nombre des cycles négatifs d'un graphe complet signé", Math. Sci. hum. 53 (1976), 63-67. | Numdam | MR 457285 | Zbl 0327.05119

[64] Toulouse G., Vannimenus J., "La frustration : un monde semé de contradictions ", La Recherche 83 (novembre 1977), 980-981.

[65] Welsh D.J.A., Matroid theory, London, Academic Press, 1976. | MR 427112 | Zbl 0343.05002

[66] Yao A.C.C., "An 0 (|E |log log |V|) algorithm for finding minimum spanning trees", Info. Froc. let. 4 (1975), 21-23. | Zbl 0307.68028

[67] Brossier G., "Représentation ordonnée des classifications hiérarchiques", Statistique et Analyse des Données 2 (1980), 31-44.