Combinatorial structures and structures for classification

Computational Statistics and Data Analysis

Volumn 23, Issue 1, 1996, Pages 169-188

  Van Cutsem, Bernard ^a  

^a Équipe VAlidation Spécification et COnstruction de logiciels   (France)

Author keywords

Combinatorial structures operations and specifications; Hierarchies; Markov chains; Partitions; Structures of classification; Uniform random generation

Indexed keywords

MARKOV PROCESSES; MATHEMATICAL MODELS; RANDOM NUMBER GENERATION;

ASYMPTOTIC PROPERTIES; COMBINATORIAL STRUCTURES;

COMBINATORIAL MATHEMATICS;

CLASSIFICATION; COMBINATORIAL STRUCTURE; MARKOV CHAIN; UNIFORM RANDOM GENERATION;

EID: 0043237202     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(96)00028-X     Document Type: Article

References (20)

1. Babai, L. and T. Lengyel, A convergence criterion for recurrent sequences with applications to the partition lattice, Analysis 12 (1992) 109-119.
2. Benzécri, J.P. et al., L'analyse des données I. La taxinomie (Dunod, Paris, 1973).
3. Comtet, L., Advanced combinatorics (Reidel, Dordrecht, 1974).
4. Critchley, F. and B. Van Cutsem, An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification, I and II, Common research report (both Department of Statistics, University of Warwick, Coventry and Laboratoire Modélisation et Calcul, IMAG, Université Joseph Fourier, Grenoble, 1992); in: B. Van Cutsem (Ed.), Classification and dissimilarity analysis, Lecture Notes in Statistics 93 (Springer, New York, 1994).
5. Critchley, F. and B. Van Cutsem, Some new useful representations of dissimilarities in mathematical classification, in: O. Opitz, B. Lausen and R. Klar (Eds.), Information and classification. Concepts, methods and applications, Studies in Classification, Data Analysis, and Knowledge Organization, Vol. 3 (Springer, New York, 1993) 132-144.
6. Flajolet, P., Mathematical methods in the analysis of algorithms and data structures, in: E. Borger (Ed.), Trends in theoretical computer sciences, Ch. 6 (Computer Science Press, Rockville, 1988) 225-304.
7. Flajolet, P., P. Zimmermann and B. Van Cutsem, A calculus for the random generation of combinatorial structures, Research Report 1830 (INRIA, 1993); Theoret. Comput. Sci, 132 (1994) 1-35.
8. Flajolet, P., P. Zimmermann and B. Van Cutsem, A calculus for the random generation of combinatorial structures, Research Report 1830 (INRIA, 1993); Theoret. Comput. Sci, 132 (1994) 1-35.
9. Harding, E.F., The probabilities of rooted tree-shapes generated by random bifurcation, Adv. Appl. Probab., 3 (1971) 44-77.
10. Hartigan, J.A., Representations of similarity matrices by trees, J. Amer. Statist. Assoc., 62 (1967) 1140-1158.
11. Jain, A.K. and R.C. Dubes, Algorithms for clustering data (Prentice-Hall, Englewood Cliffs, NJ, 1988).
12. Johnson, S.C., Hierarchical clustering schemes, Psychometrika, 32 (1967) 241-254.
13. Lengyel, T., On a recurrence involving Stirling numbers, European. J. Combin. 5 (1984) 313-321.
14. Lerman, I.C., Les bases de la classification automatique (Gauthier-Villards, Paris, 1970).
15. Murtagh, F., Counting dendrograms: a survey, Discrete. Appl. Math., 7 (1984) 191-199.
16. Nijenhuis, A. and H.S. Wilf, Combinatorial algorithms (Academic Press, New York, 1975).
17. Sneath, P.H.A. and R.R. Sokal, Numerical taxonomy (Freeman, San Francisco, 1973).
18. Van Cutsem, B. and B. Ycart, Renewal-type behaviour of absorption times in Markov chains, Adv. Appl. Probab., 26 (1994) 988-1005.
19. Vitter, J.S. and P. Flajolet, Analysis of algorithms and data structures, in: J. van Leeuwen (Ed.), Handbook of theoretical computer sciences, A : algorithms and complexity, Ch. 9 (North-Holland, Amsterdam, 1990) 431-524.
20. Zimmermann, P., Gaïa: a package for the random generation of combinatorial structures, Maple Technical Newsletter 1 (1994).