91Ó°ÊÓ

Determine the inversion sequences of the following permutations of \(\\{1,2, \ldots, 8\\}\) : (a) 35168274 (b) 83476215

Construct the permutations of \(\\{1,2, \ldots, 8\\}\) whose inversion sequences are (a) \(2,5,5,0,2,1,1,0\) (b) \(6,6,1,4,2,1,0,0\)

How many permutations of \(\\{1,2,3,4,5,6\\}\) have (a) exactly 15 inversions? (b) exactly 14 inversions? (c) exactly 13 inversions?

Bring the permutations 256143 and 436251 to 123456 by successive switches of adjacent numbers.

Build (the corners and edges of) the 4-cube, and indicate the reflected Gray code on it.

Give an example of a cyclic Gray code of order 3 that is not the reflected Gray code.

Determine the reflected Gray code of order 6 .

Determine the 7-subset of \(\\{1,2, \ldots, 15\\}\) that immediately follows \(1,2,4,6,8,14,15\) in the lexicographic order. Then determine the 7-subset that immediately precedes \(1,2,4,6,8,14,15\).

Generate the inversion sequences of the permutations of \(\\{1,2,3\\}\) in the lexicographic order, and write down the corresponding permutations. Repeat for the inversion sequences of permutations of \(\\{1,2,3,4\\}\).

Generate the 3-permutations of \(\\{1,2,3,4,5\\}\).