# Combinatorics: Zur Luria (ETH), "New bounds for the n-queen's problem"

## Location:

Title: New bounds for the n-queen's problem

Abstract:

The famous n-queens problem asks: In how many ways can n nonattacking queens be placed on an n by n chessboard? This question also makes sense on the toroidal chessboard, in which opposite sides of the board are identified. In this setting, the n-queens problem counts the number of perfect matchings in a certain regular hypergraph. We give an extremely general bound for such counting problems, which include Sudoku squares and designs.