| 摘要 |
A quick trickle permutation is one in which the spacings a?i? from the location of element i to the location of element i+1 are all different. A finite (G, DEG ) group with elements a?0? = e (the identity), a?1?,a?2?,...a?n-1? and group operation " DEG " is sequenceable if the group elements can be arranged in such an order that the partial sums (products) b?0? = a?0?, b?1? = a?0? ? DEG ? a?1?,b?2? = a?0? ? DEG ? a?1? ? DEG ? a?2?, etc., are all different. The ordered set a?0?,a?1?,a?2?,... is a sequencing, and the set of partial sums b?0?,b?1?,b?2?,... is a directed terrace. A finite group is quasi-sequenceable if an ordered set can be found in which each a?i? occurs twice, or a?i? and a?i??-1? each occur once, or a?i??-1? occurs twice and if the set of partial sums b?i? are all different. The ordered set a?0? = e, a?1?, a?2?,... is a quasi-sequencing, and the set of partial sums b?0?,b?1?,b?2?,... is a terrace. A quasi-quick trickle permutation is one in which the set of spacings, a?i?, is a quasi-sequencing. Quick trickle and quasi-quick trickle permutations are used for inter round permutations of sub-blocks or individual bits to obtain respectively row completeness or quasi row completeness in Latin squares. Sequencings, quasi-sequencings, directed terraces and terraces are used as sets of exponents of the permutations, each to be used after a different round.
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