MathDB

Pairs of subsets with certain properties

Source: Russian TST 2014, Day 10 P4 (Groups A & B)

January 8, 2024

combinatoricscounting

Problem Statement

For a natural number

n{},

determine the number of ordered pairs

(S,T)

of subsets of

\{1,2,\ldots,n\}

for which

s>|T|

for any element

s\in S

and

t>|S|

for any element

t\in T.