n個物品之直線排列數與環狀排列數有對應關係，一般而言，具有K-循環節的直線排列之所有情形數若為 ，則 即為所對應的環狀排列數，亦即每K種直線排列對應到同一種環狀排列。本文將直線排列之所有情形依所具有的K-循環節之類別做分割，並導出具有K-循環節之直線排列之所有情形數之計數公式，假設直線排列依 -循環節， -循環節， ， -循環節分類依序有 種不同排列情形，則所有的環狀排列數 。 / There exists a correspondence between ordered arrangements and circular permutations. Generally speaking, suppose the number of ordered arrangements with K-recurring periods is S, then the number of circular permutations is , namely we may assigne each K cases of ordered arrangements with K-recurring periods to a case of circular permutations. This article partitions the total cases of ordered arrangements with indistinguishable objects by means of the different catagories of K-recurring periods and derives a formula to calculate the total number of ordered arrangements with K-recurring periods. Suppose the number of ordered arrangements with -recurring periods、 -recurring periods、 、 -recurring periods is respectively, then the total number of circular permutations is .