几类组合和式的相关同余式

Congruences of Several Kinds of Combinatorics Sums

利用常数项方法,得到了几个包含常见组合序列如中心二项式系数、Catalan数、Motzkin数的部分和式的新的同余式,结合扩展的Zeilberger算法,讨论了一类含有中心二项式系数和式的同余性质之间的关系并提出了一个有待研究的问题。

By using the method of constant term, we prove several congruences of combinatorial sums in-volving some usual combinatorial sequences such as central binomial coefficients, Catalan numbers and Motzkin numbers. Moreover, with the help of the extended Zeilberger algorithm, we explore the congruence relations of a certain kind of combinatorial sums involving central binomial coefficients and propose a valuable research problem.