Title: Daniel's Flashcards / Year 4 / Term 1 / Ramsey Theory

html: Definition 1.12. If I have a combinatorial line L in [ m ] n, then I can order x ≤ y if and only if x i ≤ y i for all i. Let L − denote the first point in this ordering, and let L + denote the last point in this ordering.

html: Definition 1.13. Let L 1 , … , L k be combinatorial lines. We call them focussed if L i + = f for all i ∈ [ k ]. For a fixed colouring, they are colour focused if they are focused and L i ∖ { L i + } monochromatic for each i, and they have different colours.