论文标题
按一致的计划及其申请的持续条款
On congruence schemes for constant terms and their applications
论文作者
论文摘要
罗兰（Rowland）和Zeilberger设计了一种算法的方法，可以通过确定可表示为常数术语的组合序列值（基于Rowland和Yassawi的工作）的模量$ p^r $。由此产生的$ p $ -schemes是复发系统，取决于其形状，被归类为自动或线性。我们重新审视这种方法，提供一些其他细节，例如界限状态的数量，并提出了结合自动和线性效益的第三种自然计划。我们通过确认并扩展了Rowland和Yassawi在Motzkin数字上的猜想来说明这些“缩放”方案的实用性。
Rowland and Zeilberger devised an approach to algorithmically determine the modulo $p^r$ reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting $p$-schemes are systems of recurrences and, depending on their shape, are classified as automatic or linear. We revisit this approach, provide some additional details such as bounding the number of states, and suggest a third natural type of scheme that combines benefits of automatic and linear ones. We illustrate the utility of these "scaling" schemes by confirming and extending a conjecture of Rowland and Yassawi on Motzkin numbers.
