MathDB

Consider the set

A_n=\{x_1,x_2,\ldots,x_n,y_1,y_2,\ldots,y_n\}

2n

variables. How many permutations of set

A_n

are there for which it is possible to assign real values from the interval

(0,1)

to the

2n

variables so that: (i)

x_i+y_i=1

for each

i

; (ii)

x_1<x_2<\ldots<x_n

; (iii) the

2n

terms of the permutation form a strictly increasing sequence?

Problem Statement