| 摘要 |
<p>A quick trickle permutation is one in which the spacings ai from the location of element i to the location of element i+1 are all different. A finite (G,°) group with elements a0 = e (the identity), a1,a2,...an-1 and group operation '°' is sequenceable if the group elements can be arranged in such an order that the partial sums (products) b0 = a0, b1 = a0 ° a1,b2 = a0 ° a1 ° a2, etc., are all different. The ordered set a0,a1,a2,... is a sequencing, and the set of partial sums b0,b1,b2,... is a directed terrace. A finite group is quasi-sequenceable if an ordered set can be found in which each ai occurs twice, or ai and ai-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 a0 = e, a1, a2,... is a quasi-sequencing, and the set of partial sums b0,b1,b2,... is a terrace. A quasi-quick trickle permutation is one in which the set of spacings, ai, 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.</p> |
