User:Sopoforic/Sandbox

In the 1940's, John Riordan and Irving Kaplansky developed classical rook theory as a way to study permutations with restricted positions. In chess, a rook may move any distance along a row or column. Therefore, a permutation may be seen as an arrangement of $$n$$ rooks on an $$n\times n$$ chessboard such that none of the rooks may attack any of the others.

During the latter half of the twentieth century, and especially during the 1990's, mathematicians became increasingly interested in developing rook theory both for its own sake and for its value as a tool to solve problems in enumerative combinatorics.