Targeted Proof Machines in Combinatorics

Zeilberger 9732602 Zeilberger计划开发自动发现和证明组合学及相关领域结果的算法。特别是，他计划机械化道奇森的方法评估超几何决定因素，使用技术从计算语言学经验发现，然后严格证明'语法'的组合家庭，并制定了计算Anastomic多变量合理的生成函数。他还建议研究计算化学技术的组合类似物，并试图证明海曼的对角谐波理论。 这项研究是在组合数学的一般领域。组合数学的目标之一是找到有效的方法来研究如何安排对象的离散集合。离散系统的行为对现代通信极为重要。例如，大型网络的设计，如电话系统中的网络设计，以及计算机科学中的算法设计，都要处理离散的对象集，这就需要使用组合研究。 这项研究也是在符号计算的一般领域，试图教计算机执行以前需要大量人力资源的研究。这一领域的进展有望对科学和技术产生重要影响。

Zeilberger 9732602 Zeilberger plans to develop algorithms for automatic discovery and proof of results in combinatorics and related areas. In particular, he plans to mechanize Dodgson's method evaluating hypergeometric determinants, to use techniques from computational linguistics to empirically discover and then rigorously prove `grammars' of combinatorial families, and to develop a computational Ansatz for multi-variate rational generating functions. He also proposes to investigate combinatorial analogs of techniques from computational chemistry and to try to prove Haiman's Diagonal Harmonics conjecure. This research is in the general area of Combinatorics. One of the goals of Combinatorics is to find efficient methods of studying how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research. This research is also in the general area of Symbolic Computation, that attempts to teach computers to perform research that previously required extensive human resources. Progress in this area promises to have important ramifications to science and technology.