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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
6
votes
Acyclic categories related to structures in algebraic topology
Ralph Cohen, John Jones, and Graeme Segal found an interesting "construction" of a topological acyclic category $C(f)$ from a Morse-Smale function $f : M\to \mathbb{R}$ in a preprint in early 90's. Ob …
21
votes
What do the stable homotopy groups of spheres say about the combinatorics of finite sets?
Combinatorial descriptions of homotopy groups of spheres have been studied in the unstable world rather than the stable world.
Jie Wu found a description of homotopy groups of $S^2$ in his thesis and …