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Leprechauns on the chessboard

Publication Type: 
Refereed Original Article
Abstract: 
We introduce in this paper leprechauns, fairy chess pieces that can move either like the standard queen, or to any tile within k king moves. We then study the problem of placing n leprechauns on an n × n chessboard. When k = 1, this is equivalent to the standard n-Queens Problem. We solve the problem for k = 2, as well as for k > 2 and n ≤ (k + 1) 2 , giving in the process an upper bound on the lowest non-trivial value of n such that the (k , n)-Leprechauns Problem is satisfiable. Solving this problem for all k would be equivalent to solving the diverse n-Queens Problem, the variant of the n-Queens Problem where the distance between the two closest queens is maximized. While diversity has been a popular topic in other constraint problems, this is not the case for the n-Queens Problem, making our results the first major ones in the domain.
Digital Object Identifer (DOI): 
10.1016/j.disc.2021.112316
Publication Status: 
Published
Date Accepted for Publication: 
Friday, 15 January, 2021
Publication Date: 
01/05/2021
Journal: 
Discrete Mathematics
Volume: 
344
Institution: 
National University of Ireland, Cork (UCC)
Open access repository: 
Yes
Publication document: