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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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What proportion of chess positions that one can set up on the board, using a legal collectio...

A series of moves from the starting position to position X (therefore showing X can arrive in a legal game) is called a "proof game" and finding them is a branch of "retrograde analysis". http://en. …
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