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我们设想一个由计算机控制的机械臂,要求它做几种动作,第1种动作做m_1次,第2种动作做m_2次……第n种动作做m_n次。一种极限情形是它在做这m=∑m_j次动作时前后不受影响。确切地说机械臂每做一个动作几乎都有n种可能,除非它已经完成了某一种动作。我们自然要问,在这种简单情形下机械臂完成这m次动作有多少种不同的方式?进一步,假使机械臂在做这m次动作时前后有某种牵制,譬如说其中必须有两种动作是前后截然分开的,即必须先完成
We imagine a computer-controlled robot that requires several actions: the first action m_1 times the second action m_2 times ... the nth action m_n times. A limit case is that it does not affect before and after this m = Σm_j actions. To be precise, there are almost n possibilities for a manipulator to do one action unless it has done something. It is natural to ask how many different ways robots accomplish these m moves in this simple case. Further, if the manipulator had some sort of restraint before and after doing this m moves, say there must be two Before and after the action is completely separate, that is, must be completed