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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.

4 votes
0 answers
77 views

Minimizing the cost of clustering a hypergraph

Background and notation: Whenever I speak of a hypergraph $G$, I mean a pair of finite sets $V_G,E_G$ and a function $g\colon E_G\to\mathbb{P}(V_G)\;$ assigning each edge a subset of vertices. If $ …
David Spivak's user avatar
  • 8,659
22 votes
2 answers
459 views

Is the order on repeated exponentiation the Dyck order?

The Catalan numbers $C_n$ count both the Dyck paths of length $2n$, and the ways to associate $n$ repeated applications of a binary operation. We call the latter magma expressions; we will expl …
David Spivak's user avatar
  • 8,659