Circular Pairs - Math Problems | Repovive

Circular Pairs Beta

Let $n\ge 3$ be an integer. There are $2n$ people labeled $1,2,\ldots,2n$ , seated around a circle in this order.

In how many ways can they be divided into $n$ unordered pairs so that every group of $n$ consecutive people contains exactly one complete pair?

The seats are fixed. Pairings obtained from one another by rotation are considered different unless they consist of exactly the same pairs.

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Let $n\ge 3$ be an integer. There are $2n$ people labeled $1,2,\ldots,2n$ , seated around a circle in this order.

In how many ways can they be divided into $n$ unordered pairs so that every group of $n$ consecutive people contains exactly one complete pair?

The seats are fixed. Pairings obtained from one another by rotation are considered different unless they consist of exactly the same pairs.

You can write formulas in LaTeX or in plain text, and write your solution in any language.