自对偶克隆的刚性问题

Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000) Pub Date : 2000-05-23 DOI:10.1109/ISMVL.2000.848648

M. Miyakawa, I. Rosenberg

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引用次数: 4

摘要

自对偶克隆集合的刚性问题导致了克隆理论中的两个具体问题:(i) k={0,1，…， k-1}满足1)每个r/spl isin/ r具有相同素数长度的所有循环2)k上唯一与r的所有元素交换的一元函数是单位元e ?(1)如果一个克隆C是自动对偶克隆Pol r/sup /spl平方//，r/spl isin/ r的交叉点，并且如果它满足C/sup (1)/={e}，那么使C/sup (n)//spl sub//spl ang/J(其中J是所有投影的集合)的最小n是多少?我们对这些问题给出了部分的答案。

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Rigidity problem of autodual clones

The rigidity problem for sets of autodual clones leads to two specific problems in clone theory: (i) What are the sets R of permutations of k={0, 1,..., k-1} such that 1) each r/spl isin/R has all cycles of the same prime length and 2) the only unary function on k which commutes with all elements of R is the identity e ? () If a clone C is the inter section of the autodual clones Pol r/sup /spl square//, r/spl isin/R and if it holds C/sup (1)/={e}, what is the least n such that C/sup (n)//spl sub//spl ang/J where J is the set of all projections ? We give some partial answers to these problems.

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Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000)

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