L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, 1974. Home/Search Document Not in Database Summary Related Articles Check |
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Local Statistics Of Lattice Dimers - Kenyon (1997) (22 citations) (Correct)
....polynomial of M . Then ff k is the sum over all subsets S ae En of size k of det M S , that is, the sum over S of the probability that S is in the random matching. Let q(z) P n k=0 fi k z k where fi k is the probability that there are exactly k edges from En present. A formula of Ch. Jordan [C] relates the ff k to the fi k : fi k = ff k Gamma k 1 k ff k 1 k 2 k ff k 2 Gamma : From this we can easily derive the following: Theorem 14. We have q(z) 1 Gamma z) n p( 1 1 Gamma z ) 18 RICHARD KENYON Now if p(z) Q n i=1 (z Gamma i ) then ....
L. Comtet, Advanced combinatorics, D. Reidel Publishing Company, Dordrecht.
Entropy Computations Via Analytic Depoissonization - Jacquet, Szpankowski (1998) (Correct)
....are the coefficients of exp(x ln(1 y) Gamma xy) at x i y j , that is: 1 X i=0 1 X j=0 b ij x i y j = exp(x ln(1 y) Gamma xy) 18) such that b ij = 0 for j 2i. In fact, b ij = s 2 (j; i) j where s 2 (n; k) are the associated Stirling numbers of the first kind (cf. Comtet [4], pp. 295) Before we proceed, let us explain how one can derive formally (18) see [15] for a rigorous derivation of the error term) Observe that Taylor s expansion of e G(z) around z = n becomes e G(z) 1 X k=0 e G hki (n) z Gamma n) k k : Let us now derive a formula on the ....
....exp(x(e y Gamma 1) Gamma wy) at x i y j . More precisely: for = 1 1 X i=0 1 X j=0 a ij x i y j = exp(x(e y Gamma 1) Gamma xy) 20) and a ij = 0 for j 2i. In fact, a ij = S 2 (j; i) j where S 2 (n; k) are the 2 associated Stirling numbers of the second kind (cf. Comtet [4], pp. 222) Remark. The above can be formally re written as e G(z) exp (z(e y Gamma 1) Gamma wy) where y j = g hji (w) 21) In addition, e G hki (z) e y Gamma 1) k exp (z(e y Gamma 1) Gamma wy) where y j = g hji (w) 22) for w = z. 2 Proof. We first identify the ....
L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, Dordrecht, 1974.
Using Problem Topology in Parallelization - Liebrock (1994) (Correct)
....with p d or fewer dimensions is: j p d (n) j p d Gamma1 (n) j p d (n Gamma p d ) j p d (0) 1 j 1 (n) 1 where 2 n is the number of processors. The total number of standard processor configurations is the same as the number of partitions of an integer, n, into p d or fewer summands [Com74, NZ80] Consider a machine with 2 14 processors that is configDecomposition A SPC Time Map (32,1,1) 3483 (2,1,3) 16,2,1) 2571 (2,3,1) 8,4,1) 2128 (2,3,1) 8,2,2) 2119 (2,1,3) 4,4,2) 2113 (2,3,1) Decomposition B SPC Time Map (32,1,1) 3483 (2,1,3) 16,2,1) 2571 (2,3,1) 8,4,1) 2128 (2,3,1) ....
Louis Comtet. Advanced Combinatorics. D. Reidel Publishing Company, Boston, Mass., 1974.
A PBW Basis For Lusztig's Form Of Untwisted Affine Quantum Groups - Gavarini (1997) (Correct)
....generating series: 1 X s=0 Y s Delta i s = exp 1 X r=1 X r Delta i r ; 5:1) here i is any auxiliary symbol) notice this agree with Y 0 = 1 . This is a variation on a classical theme: the Y s s above are certain normalizations of the well known complete Bell polynomials (cf. [Co], x3.3) We shall shortly denote any change of variables given by (5.1) with Psi: X Gamma Y or X Psi Gamma Y, and then write Y= Psi (X) The converse change, to be denoted Phi: Y Gamma X or Y Phi Gamma X or X= Phi (Y) with Phi = Psi Gamma1 , is given by 1 X r=1 ....
L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, Dordrecht--Holland/Boston-- U.S.A., 1974.
On Numbers of Davenport-Schinzel Sequences - Klazar (Correct)
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L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, 1974.
Twelve Countings with Rooted Plane Trees - Klazar (1997) (1 citation) (Correct)
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L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, Dordrecht, 1974.
Hua-Huai Chern - Department Of Mathematics (Correct)
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L. Comtet, Advanced Combinatorics, The Art of Finite and In nite Expansions, D. Reidel Publishing Company, Dordrecht, Holland, 1974.
Distribution of the Number of Consecutive Records - Chern, Hwang, Yeh (2000) (Correct)
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L. Comtet, Advanced Combinatorics, The Art of Finite and Infinite Expansions, D. Reidel Publishing Company, Dordrecht, Holland, 1974.
Limit Theorems for the Number of Summands in Integer Partitions - Hwang (1997) (2 citations) (Correct)
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L. Comtet, Advanced combinatorics, the art of finite and infinite expansions, revised and enlarged edition, D. Reidel Publishing Company, Dordrecht-Holland, 1974. 29
Limit Theorems for the Number of Summands in Integer Partitions - Hwang (2000) (2 citations) (Correct)
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L. Comtet, Advanced combinatorics, the art of finite and infinite expansions, revised and enlarged edition, D. Reidel Publishing Company, Dordrecht-Holland, 1974.
Asymptotic Expansions for the Stirling Numbers of the First Kind - Hwang (1994) (3 citations) (Correct)
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L. Comtet, Advanced Combinatorics, The Art of Finite and In nite Expansions, Revised and enlarged edition, 1974, D. Reidel Publishing Company, Dordrecht-Holland.
Asymptotic Expansions for the Stirling Numbers of the First Kind - Hwang (1994) (3 citations) (Correct)
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L. Comtet, Advanced Combinatorics, The Art of Finite and Infinite Expansions, Revised and enlarged edition, 1974, D. Reidel Publishing Company, Dordrecht-Holland.
Generating Functions via Hankel and Stieltjes Matrices - Peart, Woan (2000) (6 citations) (Correct)
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L. Comtet. Advanced Combinatorics. D. Reidel Publishing Company, 1974. 12
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