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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 …
Dai Tamaki's user avatar
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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 …
Dai Tamaki's user avatar
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