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Combinatorics

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Moderate

Partitions and Non-Decreasing Lists

COMBIN-KLB19B

Consider two sets. Set $A$ is the partitions of $n$ into $k$ parts.

Set $B$ is lists $x_1, x_2, \ldots, x_k$ of positive integers such that:

$$x_1 + x_2 + \ldots + x_k = n$$

...and:

$$x_1 \geq x_2 \geq \ldots \geq x_k$$

Which is TRUE?

A

Set $A$ has more elements than Set $B$

B

Set $A$ has the same number of elements as Set $B$

C

Set $A$ has fewer elements than Set $B$

D

None of the above are true in general