| Title: | A pigeonhole principle for linear orders |
| Speaker: | Andrés Eduardo Caicedo Associate Editor Mathematical Reviews American Mathematical Society Ann Arbor, Michigan |
| Abstract: |
The basic pigeonhole principle says that if more than n items are put into n containers, then some container has at least two items. We typically consider more quantitative versions: how many items do we need if we have 3 containers, and no matter how we distribute the items, at least one container ends with 3 items? (we need at least 7.) Or, how many items do we need if we have 2 containers, and no matter how we distribute the items, either the first container ends up with 3 items, or the second one ends up with 4? (we need at least 6.)
In this talk I consider a version of this principle where we look at infinite linear orders, and consider questions such as: how large should a linear order be, if whenever it is split into two pieces, one of them contains a monotone sequence? (it suffices that the order be infinite.) Or, how large should a linear order be, if whenever it is split into two pieces, either the first piece contains an increasing sequence, or the second one contains a decreasing sequence? |
| Location: | Palenske 227 |
| Date: | 3/23/2023 |
| Time: | 3:30 PM |
@abstract{MCS:Colloquium:AndrésEduardoCaicedo:2023:3:23,
author = "{Andrés Eduardo Caicedo}",
title = "{A pigeonhole principle for linear orders}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month = "{23 March}",
year = "{2023}"
}