用于公用控制件的三元周期序列的组合计数

以组合计数理论为基础，推导出代表三位公用控制件优化方案的特殊序列（自互反、自互补、自互反且自互反补序列）数目计算公式，并给出排除等价序列（互反、互补序列）和子周期序列后的三元周期序列数目计算公式，使搜寻可用序列的基序列数目约缩为原来的１／４。进而，应用Ｓｔｉｒｌｉｎｇ渐近公式又求出当序列周期较大时各种优化序列数目的比例关系，所导出的公式不仅完善了三位公用控制件的设计理论，且使长周期可用序列的搜寻工

On the Counting of Trinary Cyclic Sequences Applied to Shared Controllers

Based on combinatorial counting theory.this peper deduces the enumeration formulae of the self reversesequences.self complementary sequences and self-mutual reverse complementary sequences. which are special sequencesrepresenting the optimization schemes of 3-position shared controllers. Enumeration formulae of the numbers of thetrinary cyclic sequence exclusive of equivalent sequences and sub-cyclic sequences are also given so as to reduce thenumber of basic sequences by a factor of 4 in searching usable sequences. Further .Stirling's asymtotic equation is appliedto finding the numbers of the optimum sequences of long cycles in proportion. All the formulae derived not only make thetheory of the shared controllers perfect, but also considerably reduce the calculations for usable sequences of long Cycles,about by two-thirds.