D. Foata, La serie generatrice exponentielle dans les problemes d'enumeration, Presses de l'Universit edeMontreal, 1974. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Enumerative Applications of a Decomposition for Graphs and Digraphs - Gessel (1993) (2 citations) (Correct)
....(#, #)ofvertices of T such that # is a descendant of # and # #.IfT has no inversions, it is called increasing.Wedefine inversions in an unrooted tree (with a totally ordered vertex set) by rooting the tree at its least vertex. The next result is due to Mallows and Riordan [14] See also Foata [5]. in I n (y) is the number of trees on [n] with i inversions. Proof. For the moment let Jm (y) for m 1, be the inversion enumerator for trees [m] rooted at vertex 1. Then the enumerator for trees on [m]rooted at i is easily seen to be y i 1 Jm (y) and thus the enumerator for all ....
D. Foata, La serie generatrice exponentielle dans les problemes d'enumeration, Presses de l'Universit edeMontreal, 1974.
Asymptotics of Poisson approximation to random discrete.. - Hwang (1998) (Correct)
....uniformity provided by the powerful singularity analysis of Flajolet and Odlyzko [35] played an important role. In this section, we start with the bivariate generating functions of several di#erent types of the parameter number of components in partitional complex and multiset constructions (cf. [36, 38, 43]) Then we review an analytic scheme originally introduced by Flajolet and Soria [36, 37] and studied in detail in Hwang [53, Ch. 5] for which we will be able to, in particular, apply our Poisson approximation formul of Theorems 1 and 2. We then state the restriction of this scheme and then go on ....
....number of components in these structures are all well approximated by suitable Poisson distributions. Consider first labeled structures. Let be a class of combinatorial structures with exponential generating function T (z) t n z n . Let be the partitional complex construction of (cf. [36, 38, 43]) We consider the following four types of number of components ( marked by w) 1. ##205 4580 The total number of L: z, w) exp(wT (z) wtnz of distinct sizes: L # (z, w) t nz in which no two components are order isomorphic: in which every ....
Foata, D. (1974) La serie generatrice exponentielle dans les problemes d'enumeration. Les Presses de l'Universite de Montreal, Montreal.
Counting Forests By Descents And Leaves - Gessel (1995) (Correct)
....of F then v and its descendents contribute to the weight of F a factor of # times the weight of the marked forest made up of the descendents of v.NowletA n,i be the number of increasing forests on [n]withi leaves. By the properties of exponential generating functions (see, for example, Foata [3], Goulden and Jackson [6, Chapter 3] or Bergeron, Labelle, and Leroux [1, Chapter 5] it follows that the exponential generating function for marked forests in which the initial forest has n vertices and i leaves is A n,i x n n (# #C) i . Asnotedintheintroduction, # i A n,i t i = A ....
D. Foata, La serie generatrice exponentielle dans les problemes d'enumeration,Pressesde l'UniversitedeMontreal, 1974.
Enumeration of Trees By Inversions - Gessel, Sagan, Yeh (1999) (5 citations) (Correct)
....satisfy the following differential equations 1. D t F o q (t) 1 1 GammaG o q (t) 2. D t F p q (t) 1 ln 1 1 GammaG o q (t) 3. D t F c q (t) 1 ln 1 1 GammaG c q (t) Proof. We shall prove the first of these identities, the others being similar. From the theory of exponential series [6, 12, 16, 20, 29] it follows that the derivative counts ordered trees with n 1 vertices (as the coefficient of t n =n ) by inversions. Removing the root of such a tree leaves an ordered forest of rooted trees. The generating function for such trees is G o q (t) where the extra factor of [n] in each term is ....
D. Foata, "La S'erie G'en'eratrice Exponentielle dans les Probl'emes d'Enum'eration," S'eminaire de Math'ematique Sup'erieurs, No. 54, Presses de l'Universit'e de Montr'eal, Montr'eal, 1974
Large Deviations for Integer Partitions - Dembo, Vershik, Zeitouni (1998) (5 citations) (Correct)
....representation by means of Bernoulli random variables are related to the combinatorial structures called selections, representations by means of Geometric random variables are related to multisets, and representations by means of Poisson random variables are related to assemblies, c.f. 10] and [8]. While the techniques of proof are similar, the details and the scalings may vary. Our choice of examples was motivated by our desire to exhibit an example of an assembly, c.f. Section 6.1, and an example of some current physical interest, c.f. Section 6.2. We distinguish between theorems where ....
D. Foata, La s'erie g'en'eratrice exponentielle dans les probl'emes d"enum'erations, Press Univ. Montreal, 1974.
Graphical Major Indices - Foata, ZEILBERGER (1995) (2 citations) Self-citation (Foata) (Correct)
....immediately from the combinatorial definition of the Stirling numbers. Accordingly, we can easily derive (1.3) and (1.4) from the vertical exponential generating function for the Stirling numbers. A more direct and conceptual proof consists of making use of the partitional complex approach [Fo74] (or invoking the theory of species dear to our qu eb ecois friends [Be94] This goes as follows. Suppose that for each r 1 there are two blocks of size r, say, the underlined [ r ] and the non underlined block [ r ] The exponential generating function for those two kinds of blocks is G = ....
Dominique Foata, "La s'erie g'en'eratrice exponentielle dans les probl `emes d"enum'eration." Montr'eal, Presses Universitaires de Montr 'eal, 1974.
Graphical Major Indices - Foata, ZEILBERGER (1995) (2 citations) Self-citation (Foata) (Correct)
....immediately from the combinatorial definition of the Stirling numbers. Accordingly, we can easily derive (1.3) and (1.4) from the vertical exponential generating function for the Stirling numbers. A more direct and conceptual proof consists of making use of the partitional complex approach [Fo74] (or invoking the theory of species dear to our Qu eb ecois friends [Be94] This goes as follows. Suppose that for each r 1 there are two blocks of size r, say, the underlined [ r ] and the non underlined block [ r ] The exponential generating function for those two kinds of blocks is G = 2 ....
Dominique Foata, "La s'erie g'en'eratrice exponentielle dans les probl `emes d"enum'eration." Montr'eal, Presses Universitaires de Montr 'eal, 1974.
The Tutte polynomial of a graph, depth-first search, and.. - Gessel, Sagan (1995) Self-citation (Foata) (Correct)
No context found.
D. Foata, "La Serie Generatrice Exponentielle dans les Problemes d'Enumeration, " Seminaire de Mathematique Superieurs, No. 54, Presses de l'Universite de Montreal, Montreal, 1974
The Tutte polynomial of a graph, depth-first search, and.. - Gessel, al. (1996) (Correct)
No context found.
D. Foata, "La S'erie G'en'eratrice Exponentielle dans les Probl`emes d'Enum'eration, " S'eminaire de Math'ematique Sup'erieurs, No. 54, Presses de l'Universit'e de Montr'eal, Montr'eal, 1974
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