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- Edward A. Bender, E. Rodney Canfield
- J. Comb. Theory, Ser. A
- 1978

Abstract Asymptotics are obtained for the number of n × n symmetric non-negative integer matrices subject to the following constraints: (i) each row sum is specified and bounded, (ii) the entries are… (More)

- Edward A. Bender
- J. Comb. Theory, Ser. A
- 1973

Abstract Let a double sequence an(k) ⩾ 0 be given. We prove a simple theorem on generating functions which can be used to establish the asymptotic normality of an(k) as a function of k. Next we turn… (More)

- Edward A. Bender
- 1974

This is an expository paper dealing with those tools in asymptotic analysis which are especially useful in obtaining asymptotic results in enumeration problems. Emphasis is on tools which are… (More)

- Edward A. Bender, E. Rodney Canfield, Brendan D. McKay
- Random Struct. Algorithms
- 1990

Let c(n, q) be the number of connected labeled graphs with n vertices and q ≤ N = (2n) edges. Let x = q/n and k = q − n. We determine functions wk ˜ 1. a(x) and φ(x) such that c(n, q) ˜… (More)

We analyze perturbation experiments performed on real and idealized ecological com- munities. A community may be considered as a black box in the sense that the individual species grow and interact… (More)

- Edward A. Bender, Zhicheng Gao, Nicholas C. Wormald
- Electr. J. Comb.
- 2002

We derive the asymptotic expression for the number of labeled 2-connected planar graphs with respect to vertices and edges. We also show that almost all such graphs with $n$ vertices contain many… (More)

- Edward A. Bender, E. Rodney Canfield
- J. Comb. Theory, Ser. A
- 1986

Abstract Let S be a surface. We asymptotically enumerate two classes of n -edged maps on S as n → ∞: rooted and rooted smooth. These are based on a system of equations which give, in principle, the… (More)

- Edward A. Bender, L. Bruce Richmond
- J. Comb. Theory, Ser. A
- 1983

Abstract Let a multivariate sequence a n (k) ⩾ 0 be given. Multivariate central and local limit theorems are proved for a n (k) as n → ∞ that are based on examining the generating function.… (More)

- Edward A. Bender
- Discrete Mathematics
- 1974

Asymptotics are obtained for the number of mxn non-negative integer matrices subject to the following constraints: (i) each row and each column sum is specified and bounded, (ii) the entries are… (More)