1.Let S ={1 , 2 ,...,n }. Apermutation a 1 a 2 ...a n of S issaidtobe...
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Question:
1.LetS={1,2,...,n}.
Apermutationa1a2...anofSissaidtobealternatingif
a1
Example:
n | AlternatingPermutations | No.ofsuchpermutations |
1 | 1 | 1 |
2 | 12 | 1 |
3 | 132,231 | 2 |
4 | 1324,1423,2314,2413,3412 | 5 |
5 | 13254,14253,14352,15243, | 16 |
| 15342,23154,24153,24351, | ||
| 25143,25341,34152,34251, | ||
| 35142,35241,45132,45231 |
Apermutationa1a2...anofSissaidtobereversealternatingif
a1>a2
Example:
| n | ReverseAlternatingPermutations | No.ofsuchpermutations |
| 1 | 1 | 1 |
| 2 | 21 | 1 |
| 3 | 312,213 | 2 |
| 4 | 4231,4132,3241,3142,2143 | 5 |
| 5 | 53412,52413,52314,51423, | 16 |
| 51324,43512,42513,42315, | ||
| 41523,41325,32514,32415, | ||
| 31524,31425,21534,21435 |
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