exponential generating function


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exponential generating function

[‚eks·pə¦nen·chəl ¦jen·ə‚rād·iŋ ′fəŋk·shən]
(mathematics)
A function, G (x), corresponding to a sequence, a0, a1, …, where G (x) = a0+ (a1 x /1!) + (a2 x 2/2!) + ⋯.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In order to use combinatorial description of (17) we interpret exp(xt) as the exponential generating function of the labelled class of sets Set(XT) (see [3, Sect.
Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity
Let [M.sub.i,k](x) be the exponential generating function of the numbers [m.sub.i,k](n).
On the number of vertices of each rank in k-phylogenetic trees
Consider the bivariate exponential generating function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the coefficient of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the number [b.sub.n,p] of basis permutations of length n in [B.sub.p].
Right-jumps & pattern avoiding permutations
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the exponential generating function for labelled bicoloured graphs.
Structure and enumeration of (3 + i)-free posets (extended abstract)
k 0 1 2 3 4 5 [p.sub.k] = dim 1 2 6 20 76 312 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] k 6 7 8 9 10 (27) [p.sub.k] = dim 1384 6512 32400 168992 921184 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] The sequence [rb.sub.k] is [?] Sequence A000898 and it is related to the number of symmetric diagrams [b.sub.k] in the Brauer algebra (21) by the binomial transform [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and thus has exponential generating function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Gelfand models for diagram algebras: extended abstract
(i) Define the exponential generating function E(z) by (4.1) (assuming it to exist at least for small [absolute value of z]).
A divergent generating function that can be summed and analysed analytically
which is the exponential generating function for the number of set partitions into blocks of size strictly bigger than 1.
Lagrange's theorem for Hopf monoids in species
The coefficients in this exponential generating function form the sequence A000262 in Sloane's Encyclopedia of Integer Sequences that counts sets of lists.
Asymptotics of smallest component sizes in decomposable combinatorial structures of alg-log type
where [B.sub.2n] [member of] Q are the Bernoulli numbers generated by the exponential generating function
Series acceleration formulas for beta values
It remains only to obtain the exponential generating function of [[micro].sub.n](a, b,1) as a ratio of cosines.
Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity
Compton's method to show that a given adequate class of finite relational structures K has a labelled 0-1 law is to show that its exponential generating function [A.sub.L](x) = [SIGMA][a.sub.L](n)[x.sup.n]/n!
Sufficient conditions for labelled 0-1 laws
(ii) Let B(x, y) be the exponential generating function enumerating the graphs in C, where x marks the vertices, and y marks the edges.
Blocks in constrained random graphs with fixed average degree
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