《易学启蒙》中的组合思想及概念

Concept of Combination in A Primer to the Study of Yi King

通过对南宋朱熹《易学启蒙》中的“卦变图”进行考究和分析，发现我国早在两宋时代，“易”学家们在卦变的研究中就处理过组合数学问题，并得到组合数学中的基本公式，经过分析论述、说明现代组合数学的思想及概念至迟在公元11世纪中叶（即北宋的李挺之时代）就在中国产生和形成了从数学史的角度来看，我国古代“先天易”学中关于排列组合理论的早期研究。

From 'Symbol-Change Diagram' in A Primer to the Study of Yi King by Zhu Xi of the South Song Dynasty, it is discovered that scholars of Yi King had already been devoted to the study of combinatorial mathematics and some of its fundamental equations were deduced. Hence, it can be stated that modern concept of combinatorial mathematics was initiated no later than the mid 11th century, and also the early study of permutations and combinations in ancient China played a leading role in the world from the mathematics historical point of view.