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

arXiv · 2201.00645

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

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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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Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, Michael Voigt. 2021-12-29. Sequences of the Stable Matching Problem. https://arxiv.org/abs/2201.00645

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