MathDB
Partitions {1,2,3,...,n}

Source: 2019 Peru Cono Sur TST P3

July 9, 2023
combinatorics

Problem Statement

Let AA be the number of ways in which the set {1,2,...,n}\{ 1, 2, . . . , n\} can be partitioned into non-empty subsets. Let BB be the number of ways in which the set {1,2,...,n,n+1}\{ 1, 2, . . . , n, n + 1 \} can be partitioned into non-empty subsets such that consecutive numbers belong to distinct subsets. Partitions that differ only in the order of the subsets are considered equal. Prove that A=BA = B.
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