Combinatoire énumérative: Proceedings of the “Colloque de by A. K. Agarwal (auth.), Gilbert Labelle, Pierre Leroux (eds.)

By A. K. Agarwal (auth.), Gilbert Labelle, Pierre Leroux (eds.)

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Extra resources for Combinatoire énumérative: Proceedings of the “Colloque de combinatoire énumérative”, held at Université du Québec à Montréal, May 28 – June 1, 1985

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And d e g r e e s This conjecture of the For integral where Bn,C n and evaluation. o f P r o b l e m and B a s i c A n a l o g restate the evaluation of I(n,S,k()) as a c o u n t i n g problem. /2 If the inner product is expanded, then all terms yield zero except for the 51 constant t e r m , and thus I(n,S,k()) where [xn]p(x) ea ([i] IT ~ES denotes the c o e f f i c i e n t of the constant term. where = un(-4)-Zk(~) xn (eia-e-ia)2k(a)), in [liP(x) denotes Our problem i s now to evaluate C ( n .

36 • if A is empty, and B has exacly one element ¥[A,B] = 0 • otherwise. Now, recall that the cardinatity of a two sorted species T is: Card(T) = T(x,y) = Z tn. k xngk/n! , summed over all n and k in IN. Card(T), and Card(~/$XT)= (S/$x)Card(T), we conclude that the cardinality of the operators X is ×, and that of $/$X is ~/$x. Note: In conformity with local traditions, we have adopted here almost the same notation for a combinatorial operator and its cardinality: we use capital letters in the "combinatorial" world and lowercase letters in the "analytical" world.

RENYI -"On a classical problem of probability theory"Publ. I. Hung. Acad. , 6(1961), 215-20 W. FELLER -"An introduction to probability theory and its applications"J. Wiley (1968) P. P. (Greece 1985) To appear in Lecture Notes in Computer Science. P. FLAJOLET, M. SOTTEAU -" Algebraic methods for trie statistics"- To appear in Annuals of Discrete Math. (1984) P. M. JACKSON-"Combinatorial Enumeration"- J. Wiley (1983) J. GOLDSTINE-"Substitution and bounded languages"- Journ of Comp. and Syst. Sciences 6 (1972) pp.

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