Chapter 6.2, Problem 49E

To determine

(a)

To prove:

thereare n + 1 terms a_{k 1} , a_{k 2} ,.. ., a_{k n + 1} with i_{k 1} = i_{k 2} =· · · = ikn+1, where 1 =k₁ < k₂ <· · · < k_{n + 1}

To determine

(b)

To prove:

a_{k j} >a_{k j + 1} for j = 1, 2,.. ., n.

To determine

(c)

To prove:

If there is no increasingsubsequence of length n + 1, then there must bea decreasing subsequence of this length.