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Sequences of the Stable Matching Problem

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arxiv 2201.00645 v1 pith:MR74RABY submitted 2021-12-29 math.HO

Sequences of the Stable Matching Problem

Matvey Borodin , Eric Chen , Aidan Duncan , Tanya Khovanova , Boyan Litchev , Jiahe Liu , Veronika Moroz , Matthew Qian
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Rohith Raghavan Garima Rastogi Michael Voigt
This is my paper
classification math.HO
keywords sequencesproblemrelatedstabledifferentdiscussintroducemarriage
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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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  1. Regular anti-phase templates in the stable marriage problem: a generator criterion, its converse, and a counting bound

    math.CO 2026-07 accept novelty 7.0

    For regular anti-phase templates P(G,A), |Stab|=n iff every adjacent quotient generates G; a coset-based lower bound is sharp for |G|≤5 and recovers f(4)=10.