login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
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

Table of n, a(n) for n=1..8.

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

Cf. A001013, A185141, A342573.

Sequence in context: A055319 A029736 A206460 * A093937 A318897 A178329

Adjacent sequences: A340887 A340888 A340889 * A340891 A340892 A340893

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 December 6 04:57 EST 2022. Contains 358594 sequences. (Running on oeis4.)