Journal of Integer Sequences, Vol. 27 (2024), Article 24.2.2

Sequences of the Stable Matching Problem


Matvey Borodin, Aidan Duncan, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt
PRIMES STEP
Department of Mathematics
MIT
77 Massachusetts Ave.
Cambridge, MA 02139
USA

Tanya Khovanova
Department of Mathematics
MIT
77 Massachusetts Ave.
Cambridge, MA 02139
USA

Abstract:

We begin this paper by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, where a man and a woman rank each other first, and 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 On-Line Encyclopedia of Integer Sequences.


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(Concerned with sequences A000142 A001044 A002860 A091868 A185141 A338665 A340890 A342573 A343474 A343475 A343692 A343693 A343694 A343695 A343696 A343697 A343698 A343699 A343700 A344662 A344663 A344664 A344665 A344666 A344667 A344668 A344669 A344670 A344671 A344689 A344690 A344691 A344692 A344693 A345679 A351413.)


Received January 10 2022; revised versions received September 22 2023; October 29 2023; January 15 2024. Published in Journal of Integer Sequences, January 16 2024.


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