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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.
3
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Conceptual reason why the sign of a permutation is well-defined?
It is related to the Steenrod operation $\mathrm{Sq}^2$ vanishing in the cohomology of the sphere spectrum.
This vanishing is witnessed by a spectrum map $\sigma: S \to E$, where $E$ is the fiber of a …