# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, November 22, 2018, 12:15 pm

**Duration**: 45 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Justin Dallant

## A Simply Exponential Upper Bound on the Maximum Number of Stable Matchings

This talk is based on a 2017 paper by Anna R. Karlin, Shayan Oveis Gharan and Robbie Weber.

Suppose you are given two sets of respectively n men and n women, where each man ranks all the women based on his preference and reciprocally each woman ranks all the men. A matching is a bijection between these two sets, and it is stable if there is no unmatched man/woman pair where both the man and the woman would rather be matched together than with their current match.

Before this paper, the best known bounds on f(n), the maximum number of stable matchings that a stable matching instance with n men and n women can have, were roughly 2.28^{n} ≤ f(n) ≤ 2^{n·log(n)-O(n)}. I will present the new upper bound of c^{n} for some constant c along with its proof, which relies on the correspondence between stable matchings of an instance and downsets of a particular poset called the rotation poset of that instance.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login