MathDB

assume that X is a set of n number.and

0\leq k\leq n

.the maximum number of permutation which acting on

X

st every two of them have at least k component in common,is

a_{n,k}

.and the maximum nuber of permutation st every two of them have at most k component in common,is

b_{n,k}

. a)proeve that :

a_{n,k}\cdot b_{n,k-1}\leq n!

b)assume that p is prime number,determine the exact value of

a_{p,2}

Problem Statement