Geodesic
A q-queens problem. VI. The bishops' period
Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 549-561.

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The number of ways to place q nonattacking queens, bishops, or similar chess pieces on an n × n square chessboard is essentially a quasipolynomial function of n (by Part I of this series). The period of the quasipolynomial is difficult to settle. Here we prove that the empirically observed period 2 for three to ten bishops is the exact period for every number of bishops greater than 2. The proof depends on signed graphs and the Ehrhart theory of inside-out polytopes.
DOI : 10.26493/1855-3974.1657.d75
Keywords: Nonattacking chess pieces, Ehrhart theory, inside-out polytope, arrangement of hyperplanes, signed graph 
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Seth Chaiken; Christopher R. H. Hanusa; Thomas Zaslavsky. A q-queens problem. VI. The bishops' period. Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 549-561. doi : 10.26493/1855-3974.1657.d75. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1657.d75/

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