University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > The n-queens problem

## The n-queens problemAdd to your list(s) Download to your calendar using vCal - Candida Bowtell, Birmingham
- Thursday 09 December 2021, 15:30-16:30
- LTA, additional zoom link: https://bham-ac-uk.zoom.us/j/87124623071 (NOTE: UNUSUAL TIME).
If you have a question about this talk, please contact Johannes Carmesin. How many ways are there to place n queens on an n by n chessboard so that no two can attack one another? What if the chessboard is embedded on the torus? Let Q(n) be the number of ways on the standard chessboard and T(n) the number on the toroidal board. The toroidal problem was first studied in 1918 by PĆ³lya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne In this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. This is joint work with Peter Keevash. This talk is part of the Combinatorics and Probability Seminar series. ## This talk is included in these lists:- Combinatorics and Probability Seminar
- LTA, additional zoom link: https://bham-ac-uk.zoom.us/j/87124623071 (NOTE: UNUSUAL TIME)
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