The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A340890 a(n) is the number of preference profiles for n men and n women, where all men prefer the same woman. 5
1, 8, 5184, 1719926784, 990677827584000000, 2495937495082991616000000000000, 58001506007267709490243656115814400000000000000, 23264754073069200132851692722771970253637181903994880000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This is the same number of preference profiles as when all men rank the same woman at the i-th place, where i can be anywhere from 1 to n.
Note that we can swap men and women in the definition of the sequence.
The total number of possible profiles is A185141.
a(n) = n!^n A342573(n), where A342573 ignores women's preferences.
a(n) is a subsequence of A001013.
LINKS
Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, Sequences of the Stable Matching Problem, arXiv:2201.00645 [math.HO], 2021.
FORMULA
a(n) = n(n-1)!^n * n!^n.
EXAMPLE
When n=2, the total number of profiles is 16, and in half of them, the same woman is ranked 1st by both men.
MATHEMATICA
Table[n (n - 1)!^n n!^n, {n, 10}]
CROSSREFS
Sequence in context: A055319 A029736 A206460 * A093937 A318897 A178329
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, Mar 31 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)