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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.

35 votes

Why do wedges of spheres often appear in combinatorics?

This is indeed a mystery. I presume the question refers to wedges of spheres of the same dimension, where there's a simple criterion (n-dimensional and (n-1)-connected, for some n). For wedges of sph …
Allen Hatcher's user avatar
4 votes
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Discriminants of indefinite integral binary quadratic forms admitting 3 or 6 torsion.

The structure of the automorphism group becomes clear when one looks at the Conway topograph of a given form. For an indefinite form not representing 0 the topograph has an infinite periodic river se …
Allen Hatcher's user avatar