MathDB

Let

n\in N

n\geq2

and the set

X

with

n+1

elements. The ordered sequences

(a_{1}, a_{2},\ldots,a_{n})

and

(b_{1},b_{2},\ldots b_{n})

of distinct elements of

X

are said to be

<span class='latex-italic'>separated</span>

if there exists

i\neq j

such that

a_{i}=b_{j}

. Determine the maximal number of ordered sequences of

n

elements from

X

such that any two of them are

<span class='latex-italic'>separated</span>

. Note: ordered means that, for example

(1,2,3)\neq(2,3,1)

Problem Statement