摘要翻译：
设\svec=(s_1,...,s_m)和\tvec=(t_1,...,t_n)是m,n的非负整数值函数的向量，且S=sum_{i=1}^m s_i=sum_{j=1}^n t_j相等。设M(\svec,\tvec）为具有非负整数项的M*n个矩阵的个数，使得对于所有i,j,第i行具有行和s_i,第j列具有列和t_j。这种矩阵出现在许多不同的设置中，一个重要的例子是统计中重要的列联表（也称为频率表）。定义S=max_i s_i和T=max_j T_j。以前的工作已经证明了M(\svec，\tvec)的渐近值为M,n\to\infty，s和t有界（各作者独立，1971-1974),当\svec，\tvec为M/n,n/M,s/n>=c/log n时（Canfield and McKay,2007）。本文将稀疏范围推广到ST=O(S^(2/3))的情形。该证明部分遵循了先前在相同条件下0-1矩阵的渐近枚举(Greenhill,McKay and Wang,2006）。我们还将枚举推广到包含0和1的非负整数的任意子集上的矩阵。
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英文标题：
《Asymptotic enumeration of sparse nonnegative integer matrices with
  specified row and column sums》
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作者：
Catherine Greenhill and Brendan D. McKay
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最新提交年份：
2012
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分类信息：

一级分类：Mathematics        数学
二级分类：Combinatorics        组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Let \svec = (s_1,...,s_m) and \tvec = (t_1,...,t_n) be vectors of nonnegative integer-valued functions of m,n with equal sum S = sum_{i=1}^m s_i = sum_{j=1}^n t_j. Let M(\svec,\tvec) be the number of m*n matrices with nonnegative integer entries such that the i-th row has row sum s_i and the j-th column has column sum t_j for all i,j. Such matrices occur in many different settings, an important example being the contingency tables (also called frequency tables) important in statistics. Define s=max_i s_i and t=max_j t_j. Previous work has established the asymptotic value of M(\svec,\tvec) as m,n\to\infty with s and t bounded (various authors independently, 1971-1974), and when \svec,\tvec are constant vectors with m/n,n/m,s/n >= c/log n for sufficiently large (Canfield and McKay, 2007). In this paper we extend the sparse range to the case st=o(S^(2/3)). The proof in part follows a previous asymptotic enumeration of 0-1 matrices under the same conditions (Greenhill, McKay and Wang, 2006). We also generalise the enumeration to matrices over any subset of the nonnegative integers that includes 0 and 1.
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PDF链接：
https://arxiv.org/pdf/707.034