Sur quelques aspects combinatoires du calcul des probabilités
Letac, Gérard
Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 49 (1972), p. 1-82 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1972-01-01
@article{ASCFM_1972__49_8_A1_0,
     author = {Letac, G\'erard},
     title = {Sur quelques aspects combinatoires du calcul des probabilit\'es},
     journal = {Annales scientifiques de l'Universit\'e de Clermont. Math\'ematiques},
     volume = {49},
     year = {1972},
     pages = {1-82},
     mrnumber = {482985},
     zbl = {0251.60036},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASCFM_1972__49_8_A1_0}
}

Letac, Gérard. Sur quelques aspects combinatoires du calcul des probabilités. Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 49 (1972) pp. 1-82. http://gdmltest.u-ga.fr/item/ASCFM_1972__49_8_A1_0/

[1] Ash Robert "Information theory" chapitre 2 Interscience Wiley (New-York) 1965 | MR 229475 | Zbl 0768.94005

[2] Banach Stefan "On measures of independent fields" Studia Mathematica, vol. 10 (1948) pp. 159-181 | MR 29422 | Zbl 0037.03703

[3] Dubins Lester E. "On a theorem of Skorohod" Annals of Mathematical Statistics, vol. 39 (1968) pp. 2094-2097 | MR 234520 | Zbl 0185.45103

[4] Van Kampen "Infinite products measures and infinite convolutions " American Journal of Mathematics, vol. 62 (1940) pp. 417-448 | JFM 66.0220.02 | MR 1282

[5] Kolmogorov A. "Sur les propriétés des fonctions de concentration de M. Paul Lévy" Annales de l'Institut Henri Poincaré, XVI, vol. 1, pp. 27-34 (1958) | Numdam | MR 101545 | Zbl 0105.11804

[6] Letac Gérard "Problèmes de probabilité". Problème n° 19 - P.U.F. (1970) | Zbl 0206.19604

[7] Lubell David "A short proof of Sperner lemma" Journal of combinatorial theory, vol. 1 (1966) pp. 299 | MR 194348 | Zbl 0151.01503

[8] Meyer Paul-André "Séminaire de probabilités IV de l'Université de Strasbourg" (pp.134) Lectures Notes in Mathematics n° 124 - SPRINGER VERLAG, Berlin (1970)

[9] Renyi Alfred "Calcul des Probabilités" page 71, DUNOD (Paris) 1966 | MR 202161 | Zbl 0141.14702

[10] Renyi Alfred "Foundations of probability" page 167 Holden Day, San Francisco (1970) | MR 264723 | Zbl 0203.49801

[11] Rohrlin V.A. "On the fundamental ideas of measure theory" In "Translations, série 1, vol. 10, Functional analysis and measure theory" A.M.S. Rhode Island (1962)

[12] Skorokhod A.V. "Studies in the theory of random processes" page 163 Addison-Wesley (Reading) (1965) | MR 185620 | Zbl 0146.37701

[1] Bernard Jacques et Letac Gérard "Construction d'évènements équiprobables et coefficients multinomiaux module pn" A paraître à l'Illinois Journal of Mathematics | Zbl 0294.60011

[2] Carlitz Léonard "Sequences and Inversions" Duke Mathematical Journal, vol. 37 n° 1 (1970) pp. 193-198 | MR 252237 | Zbl 0206.02302

[3] Comtet Louis "Analyse combinatoire" Tome 2, page 108 - P.U.F. (1970) | Zbl 0221.05001 | Zbl 0221.05002

[4] Fray Robert D. "Congruences properties of ordinary and q - binomial coefficients" Duke Mathematical Journal, vol. 34 (1967) | MR 213287 | Zbl 0155.08303

[5] Hering "Eine Beziehung zwishen Binomialkoeffizienten und Primzahlpotenzen" Archiv für Mathematik, vol. 19 (1968) pp. 411-412 | MR 232687 | Zbl 0162.05804

[6] Hermite Charles cité par L.E. Dickson in "History of the theory of numbers" vol. 1, chapitre 6 G.E. STECHERT (New-York) (1934)

[7] Letac Gérard "Sur certains polynômes à coefficients positifs " Comptes rendus de l'Académie des Sciences, vol. 269 (3.12.69) pp. 1066-1068 | MR 258646 | Zbl 0186.30201

[8] Mac Mahon P.A. "The indices of permutations and the derivation there from of functions of a single variable associated with the Permutations of any Assemblage of Objects" American Journal of Mathematics, vol. 48, tome 4 (1913) pp. 282-321 | JFM 44.0076.02

[9] Meynieux Robert "Sur le plus petit commun multiple des coefficients du polynôme (1+z)n et celui de certains de ces coefficients" Comptes rendus de l'Académie des Sciences, vol. 271 (2.10-1970) pp. 861-864 | MR 271009 | Zbl 0207.02402

[10] Polya Georges "On the number of certain lattice polygons" Journal of Combinatorial Theory, vol. 6 (1969) pp. 102-105. | MR 236031 | Zbl 0327.05010

[11] Sylvester J.J. "A constructive theory of partitions, arranged in three acts, an interact and an exodion" American Journal of Mathematics, vol. 5 (1882) pp. 251-330 | JFM 15.0129.02 | MR 1505328

[1] Austin T.L. "The enumeration of point labelled chromatic graphs and trees" Canadian Journal of Mathematics, vol. 12 (1960), pp. 535-545 | MR 139544 | Zbl 0096.17802

[2] Barra Jean-René Notions fondamentales de Statistique Mathématique. Dunod (1971) | MR 402992 | Zbl 0257.62004

[3] Bass Jean "Sur la compatibilité des fonctions de répartition" Comptes rendus de l'Académie des Sciences, vol. 240 (1965) pp. 839-843 | MR 68149 | Zbl 0064.12804

[4] Berge Claude "Théorie des graphes et applications". Dunod (1958) | MR 102822 | Zbl 0088.15404

[5] Billingsley Patrick "Ergodic Theory and Information". Wiley (New-York) (1965) | MR 192027 | Zbl 0141.16702

[6] Buck, R. Creighton "Linear Spaces and approximation theory" in "On numerical Approximation", R.E. LANGER Editeur, publié par les University of Wisconsin Press (1958) pp. 11-23 | MR 101611 | Zbl 0083.28801

[7] Cartier, Pierre

[8] Choquet, Gustave "Le problème des Moments". Séminaire d'Initiation à l'Analyse, 1ère année. Secrétariat Mathématique de l'I.H.P. (Paris) 1962 | Numdam | Zbl 0121.33103

[9] Diliberto, S.P. et Straus, E.G. "On the approximation of a function of several variables by the sum of functions of fewer variables". Pacific Journal of Mathematics, Vol. 1 (1951) pp. 195-210 | MR 43882 | Zbl 0043.06801

[10] Djokovic D.Z. "Extreme points of certain convex polytopes ". Monatshefte für Mathematik, Band 69, Heft 5 (1965), pp. 385-388 | MR 193100 | Zbl 0151.28901

[11] Douglas, R.G. "On extremal measures and subspace density ". Michigan Mathematical Journal, 11 (1964), pp. 243-46 | MR 185427 | Zbl 0121.33102

[12] Feller William "An introduction to probability theory and its applications" Vol. 1, 3rd edition, Wiley (New-York) (1968) | MR 228020 | Zbl 0077.12201

[13] Fishburn Peter J.; "Additive representations of Real functions on product sets" Journal of combinatorial theory. Vol. 4, n° 4 (1968) pp. 397-402 | MR 218251 | Zbl 0159.30203

[14] Foata, D. et Schutzenberger, M. "Théorie géométrique des polynômes eulériens " Lecture notes, vol. 138. Springer Verlag (Berlin), 1970 | MR 272642 | Zbl 0214.26202

[15] Frechet Maurice "Sur les tableaux de corrélation dont les marges et les bornes sont données". Annales de l'Université de Lyon, 3ème série, Sciences, section A, 1958, pp. 19-32 | MR 110128 | Zbl 0095.13603

[16] Hennequin P.L. et Tortrat A. "Théorie des probabilités et quelques applications " Masson (Paris), 1965 | MR 178481 | Zbl 0128.37403

[17] Letac Gérard "Problèmes de Probabilité", problème n° 70 Presses Universitaires de France, Paris (1970) | Zbl 0206.19604

[18] Letac Gérard "Représentation des mesures de probabilité de deux espaces dénombrables, de marges données" Illinois Journal of Mathematics, vol. 10, n° 3, Sept. 1966, pp. 497-507 | MR 200957 | Zbl 0141.14801

[19] Lindenstrauss Joram "A remark on extreme doubly stochastic measures" American Mathematical Monthly 72, 4 (1965) pp. 379-382 | MR 181728 | Zbl 0152.24404

[20] M R., Mycielski J. and Thompson D. "On Boolean functions and connected sets". Mathematical systems theory, vol. 5, n° 3 (1971), pp. 259-270 | MR 423902 | Zbl 0221.02047

[21] Meyer Paul-André "Probabilité et Potentiel". HERMANN (Paris) 1966 | MR 205287 | Zbl 0138.10402

[22] Pham Dinh Tuan "Contributions à l'Analyse de la variance et aux plans d'expérience". Thèse de spécialité. Grenoble 1970.

[23] Phelps, Robert B. "Lectures on Choquet's theorem". VAN NOSTRAND (New-York) 1966 | MR 193470 | Zbl 0135.36203

[24] Rado R. "On a combinatorial theorem on vector spaces" Journal of London Mathematical society (1962) | MR 146186 | Zbl 0106.01203

[25] Ryser Herbert-John "Combinatorial Mathematics". Carus mathematical monographs, Wiley (New-York) 1965 | MR 150048 | Zbl 0112.24806 | Zbl 0302.05001

[26] Scoins " The number of trees with modes of alternate parity" Proceedings of Cambridge Philosophical Society 58 (1962) pp. 12-18 | MR 136554 | Zbl 0122.41901

[27] Strassen Victor "The existence of probability measures with given marginals" Annals of Mathematical Statistics. Vol. 36 (1965), pp. 423-439 | MR 177430 | Zbl 0135.18701

[28] Tits Jacques "Sur le groupe des automorphismes d'un arbre" In "Mémoires dédiés à Georges de Rham" pp. 188-211, Springer Verlag, Berlin 1970 | MR 299534 | Zbl 0214.51301

[29] Varopoulos Nicolas "Tensor algebras and Harmonic analysis ". Acta Mathematica 119 (1967), pp. 51-112 | MR 240564 | Zbl 0163.37002

[30] Vorobev, N.N. "Consistent families of measures and their extensions" Theory of Probability and its applications. Vol. 7, n° 2 (1962) pp. 147-163. | Zbl 0201.49102