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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.
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OEIS Sequence A002846 and properties of matrix inverses
Sequence A002846 in https://oeis.org/A002846 (OEIS) gives, for each positive integer $n$, the number $a(n)$ of ways of transforming a set of $n$ indistinguishable objects into $n$ singletons via a seq …
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OEIS Sequence A002846 and properties of matrix inverses
Actually, this turned out to be embarrassingly simple. Let $M$ be such an $n\times{}n$ matrix and set $\mathbf{i}_n$ to be the column matrix with entries 1 to $n$ and $\mathbf{1}_n$ to be the column m …