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Results tagged with co.combinatorics
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user 175589
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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What is this invariant graph?
Let $G$ be a simple graph (finite or infinite), $[n]\mathrel{:=}\{1,...,n\}$. Define the function:
$$\varepsilon_n(G)\mathrel{:=}\min_\phi{\lvert{\operatorname{dom} (\phi)}\rvert},$$
where $\phi$ is t …
- 107
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The quantity of poset with a given number of pairs of incomparable elements
$\DeclareMathOperator\inc{inc}$Let $|X|=n$ and $\inc(X,\leq)=\{\{x,y\} : \neg (x\leq y)\wedge \neg (y\leq x)\}$, where $(X,\leq)$ is poset (possibly unconnected). Define the function:
$$\pi(n,m):=|\{ …
- 107