Small random instances of the stable roommates problem

TL;DR

This paper derives an explicit formula for the probability that a random stable roommates problem instance of size n has a solution, and computes exact probabilities for small sizes up to n=12.

Contribution

It provides a new explicit formula for the probability of solvability in the stable roommates problem and calculates exact values for small instances.

Findings

Explicit formula for p_n derived

Exact probabilities computed for n ≤ 12

Probability of solvability varies with n

Abstract

Let $p_n$ denote the probability that a random instance of the stable roommates problem of size $n$ admits a solution. We derive an explicit formula for $p_n$ and compute exact values of $p_n$ for $n\leq 12$.