2023/12/07 by Morrison, Ralph, Speeter, Noah
#05C57 #05C69 #14T99 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.04686
In this paper we study queen's graphs, which encode the moves by a queen on an n× m chess board, through the lens of chip-firing games. We prove that their gonality is equal to nm minus the independence number of the graph, and give a one-to-one correspondence between maximum independent sets and classes of positive rank divisors achieving gonality. We also prove an identical result for toroidal queen's graphs.