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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