Sequences of the Stable Matching Problem
Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan, Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima, Rastogi, Michael Voigt
TL;DR
This paper explores various preference profiles in the stable marriage problem, introduces new sequences related to soulmate and hell-pair configurations, and analyzes the egalitarian cost of matchings.
Contribution
It introduces 30 new sequences related to preference profiles and discusses existing sequences, expanding the combinatorial understanding of the stable marriage problem.
Findings
Generated sequences for different preference profile types
Analyzed sequences related to egalitarian cost of matchings
Connected new sequences to existing OEIS sequences
Abstract
In this paper, we begin by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, which are a man and a woman who rank each other first. Inversely, we examine hell-pairs, where a man and a woman rank each other last. We generate sequences enumerating preference profiles of different types. We also calculate sequences related to the egalitarian cost, or "quality", of a matching. In total, we introduce and discuss 30 new sequences related to the stable marriage problem and discuss 6 sequences that are already in the OEIS.
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Taxonomy
TopicsGame Theory and Voting Systems