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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
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answers
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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 $ …
22
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2
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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 …