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We obtain the asymptotic number of labelled tournaments with a given score sequence in the case where each score is n/2 + O(n 3/4+ǫ) for sufficiently small ǫ > 0. Some consequences for the score sequences of random tournaments are also noted. The method used is integration in n complex dimensions.

Let s = (s 1 ,. .. , s m) and t = (t 1 ,. .. , t n) be vectors of non-negative integer-valued functions with equal sum S = m i=1 s i = n j=1 t j. Let N (s, t) be the number of m × n matrices with entries from {0, 1} such that the ith row has row sum s i and the jth column has column sum t j. Equivalently, N (s, t) is the number of labelled bipartite graphs… (More)

- Xiaoji Wang
- 2003

1. Abstract. We consider the estimation of the number of labelled eulerian digraphs with multiple edges by using an n-dimensional Cauchy integral. The asymptotic value is obtained for any fixed bound on the multiplicity of an edge. 2. Main result. By an eulerian digraph we mean a digraph in which the in-degree is equal to the out-degree at each vertex. Let… (More)

In the present paper, we report an efficient total synthesis of a marine alkaloid, rigidin E. The key tetrasubstituted 2-amino-3-carboxamidepyrrole intermediate was synthesized by cascade Michael addition/intramolecular cyclization between N-(2-(4-(benzyloxy)phenyl)-2-oxoethyl)methanesulfonamide and 3-(4-(benzyloxy)phenyl)-2-cyano-N-methylacrylamide.… (More)

- Xiaoji Wang, Chanshan Lv, Junmin Feng, Linjun Tang, Zhuo Wang, Yuqing Liu +3 others
- Marine drugs
- 2015

Itralamides A and B were isolated from the lipophilic extract of Lyngbya majuscula collected from the eastern Caribbean. Itralamide B (1) showed cytotoxic activity towards human embryonic kidney cells (HEK293, IC50 = 6 μM). Preliminary studies disapproved the proposed stereochemistry of itralamide. In this paper, we will provide a full account of the total… (More)

- Xiaoji Wang
- 2003

We determine some explicit expressions for the costs of Huffman trees with several classes of weight sequences.

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