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Generate Permutations

What Type?
All permutations of [n] = {1,2,..., n}.   [IMG = Green Check]  
All k-permutations of {1,2,...n}.   [IMG = Green Check]  
All permutations [n] by Transpositions   [IMG = Green Check]  
Derangements of [n], [with k cycles].   [IMG = Green Check]  
Involutions of [n].   [IMG = Green Check]  
With k cycles.   [IMG = Green Check]  
With given cycle structure, (ni = number of i cycles.)   [IMG = Green Check]  
With maximum cycle length k.   [IMG = Green Check]  
With k left to right maxima.   [IMG = Green Check]  
With given ups and downs.   [img Red-x]  
Stamp Foldings, restricted to   [IMG = Green Check]  
Permutations of [n] with k inversions   [IMG = Green Check]  
Permutations of [n] with index k   [IMG = Green Check]  
Dumont (Genocchi) sequences of the first kind   [IMG = Green Check]  
Dumont (Genocchi) sequences of the second kind   [IMG = Green Check]  

Input: (1 <= k <= n <= 50)
(0 <= k <= C(n,2) for Inversions and Index)
n =
k =

Cycle Structure Information:
n1 =
n2 =
n3 =
n4 =
n5 =
n6 =

Output:
One line notation   [IMG = Green Check]  
Cycle notation   [IMG = Green Check]  
Transposition (if applicable)   [IMG = Green Check]  
Permutation matrix (chess board)   [IMG = Green Check]  
Inverse Permutation   [IMG = Green Check]  
Standard Young Tableau   [IMG = Green Check]  
Diagram (if applicable)   [IMG = Green Check]  


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