We study systems of equations on antichains, together with a way to count the number of solutions. We start with two simple examples, generalise and show more applications. One of the results was used in the recent computation of D(9), the others have potential to speed up existing techniques in the future.

翻译：本研究探讨了基于反链的方程组及其解的计数方法。我们从两个简单示例出发，进行一般化推广并展示更多应用场景。其中一项成果已应用于近期第九戴德金数D(9)的计算实践，其余方法则有望在未来优化现有计算技术。