MathDB

Let m be a positive integer. An

m

-pattern is a sequence of

m

symbols of strict inequalities. An

m

-pattern is said to be realized by a sequence of

m + 1

real numbers when the numbers meet each of the inequalities in the given order. (For example, the

5

-pattern

<, <,>, < ,>

is realized by the sequence of numbers

1, 4, 7, -3, 1, 0

.) Given

m

, which is the least integer

n

for which there exists any number sequence

x_1,... , x_n

such that each

m

-pattern is realized by a subsequence

x_{i_1},... , x_{i_{m + 1}}

with

1 \le i_1 <... < i_{m + 1} \le n

Problem Statement