A generalization of the birthday problem

February 3, 2012
Sukhada Fadnavis | Stanford University

The birthday problem states that there is at least half a chance that some two out of twenty-three randomly chosen people will share the same birth date. The calculation for this problem assumes that all birth dates are equally likely. What if the distribution of birth dates is non-uniform and possibly even unknown? Further what if we focus on birthdays shared by two friends rather than any two people? I will present some of our results and conjectures in this generalized setting. I will also show how these results are related to the Stanley-Stembridge poset chain conjecture and the ‘shameful conjecture’, two famous conjectures in combinatorics.

Speaker Details

Sukhada is a PhD candidate in mathematics at Stanford University working under the guidance of Professor Persi Diaconis. She completed her bachelors degree in mathematics from Caltech. Her research interest lies in discrete mathematics with experience in graph colorings, random graph models, graph limits and mixing times of Markov chains.