J. A. Fill, P. Flajolet, and N. Kapur. Singularity analysis, Hadamard products, and Tree recurrences, 2003, arXiv:math.CO/0306225. Submitted for publication. Home/Search Document Not in Database Summary Related Articles Check |
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Transfer Theorems and Asymptotic Distributional Results m-ary.. - Fill, Kapur (2004) (3 citations) Self-citation (Fill Kapur) (Correct)
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J. A. Fill, P. Flajolet, and N. Kapur. Singularity analysis, Hadamard products, and Tree recurrences, 2003, arXiv:math.CO/0306225. Submitted for publication.
Limiting Distributions For Additive Functionals On Catalan Trees - Fill, Kapur (2004) Self-citation (Fill Kapur) (Correct)
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J. A. Fill, P. Flajolet, and N. Kapur. Singularity analysis, Hadamard products, and Tree recurrences, 2003, arXiv:math.CO/0306225. Submitted for publication.
ICM 2002 Vol. III 1-3 - Singular Combinatorics Philippe Self-citation (Flajolet) (Correct)
....closed under di erentiation and integration. Finally, the Hadamard product of two series, f g is de ned as the termwise product: f(z) g(z) n fn g n z , if f(z) g(z) Hadamard (1898) proved that singularities get composed multiplicatively. Finer composition properties [4] result from an adaptation of Hankel contours to Hadamard s formula f(z) g(z) 1 f(t)g w dt t : Theorem 5 Functions of S.A. type are closed under Hadamard product. Example 4. Divide and conquer algorithms solve recursively a problem of size n by splitting it into two subproblems ....
....One then has in operator notation f(z) I L) t] z) where the quasi inverse acts as a singularity transformer . Closure theorems allow for an asymptotic classi cation of the cost functions induced by various tolls under various probabilistic models mirrored by the splitting probabilities [4]. 4. Functional equations Algebraic functions have expansions at singularities that are expressed by fractional power series (Newton Puiseux) Consequently, they are of S.A. type with rational exponents; accordingly their coecient expansions are linear combinations of algebraic elements of the ....
James A. Fill, Philippe Flajolet, and Nevin Kapur, Singularity Analysis, Hadamard Products, and Trees Recurrences, Preprint, 2002.
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