Bootcamp 6 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp (6 of 6)

Lecturer: Jaroslav Nesetril

Date: Monday October 3, 2016.

Main Topics: Other applications of the “product argument”, Chain-Ramsey for Posets, Proof of edge-Ramsey for Graphs, Proof of Hales-Jewett

Definitions: Structural pigeonhole principle, Poset, Graph product, Combinatorial line

Bootcamp 1 – Bootcamp 2 – Bootcamp 3Bootcamp 4Bootcamp 5 – Bootcamp 6
Continue reading Bootcamp 6 – Ramsey DocCourse Prague 2016

Contest Pigeons!

(This is a talk I gave for the Canadian IMO team at their 2014 winter camp at York University on Jan 3, 2014.)

The pigeonhole principle is a remarkable combinatorial theorem that looks silly and obvious, but turns out to be quite powerful and useful, especially in the context of contest problem solving. I’m going to present a couple of statements of the pigeonhole principle, then I’ll give some broad applications of it. I’ll end off with a list of problems.

Found them!

Continue reading Contest Pigeons!