@article{chaiken-queens,
author = {Chaiken, Seth and Hanusa, ChristopherR.H. and Zaslavsky, Thomas},
title = {A q-Queens Problem. II. The square board},
year = {2015},
journal = {Journal of Algebraic Combinatorics},
pages = {619-642},
doi = {10.1007/s10801-014-0547-0},
issn = {0925-9899},
keywords = {Nonattacking chess pieces; Fairy chess pieces; Ehrhart theory; Inside-out polytope; Arrangement of hyperplanes; Primary 05A15; Secondary 00A08; 52C35},
language = {English},
number = {3},
publisher = {Springer US},
url = {http://dx.doi.org/10.1007/s10801-014-0547-0},
volume = {41},
}
@article{Bell20091,
author = {Jordan Bell and Brett Stevens},
title = {A survey of known results and research areas for -queens},
year = {2009},
journal = {Discrete Mathematics},
pages = {1 - 31},
abstract = {In this paper we survey known results for the n -queens problem of placing n nonattacking queens on an n x n chessboard and consider extensions of the problem, e.g.Â other board topologies and dimensions. For all solution constructions, we either give the construction, an outline of it, or a reference. In our analysis of the modular board, we give a simple result for finding the intersections of diagonals. We then investigate a number of open research areas for the problem, stating several existing and new conjectures. Along with the known results for n -queens that we discuss, we also give a history of the problem. In particular, we note that the first proof that n nonattacking queens can always be placed on an n x n board for n > 3 is by E. Pauls, rather than by W. Ahrens who is typically cited. We have attempted in this paper to discuss all the mathematical literature in all languages on the n -queens problem. However, we look only briefly at computational approaches.},
doi = {http://dx.doi.org/10.1016/j.disc.2007.12.043},
issn = {0012-365X},
keywords = {Chessboard problems},
number = {1},
url = {http://www.sciencedirect.com/science/article/pii/S0012365X07010394},
volume = {309},
}
@article{Hsiang200487,
author = {Jieh Hsiang and D.Frank Hsu and Yuh-Pyng Shieh},
title = {On the hardness of counting problems of complete mappings},
year = {2004},
journal = {Discrete Mathematics},
pages = {87 - 100},
abstract = {A complete mapping of an algebraic structure (G,+) is a bijection f(x) of G over G such that f(x)=x+h(x) for some bijection h(x). A question often raised is, given an algebraic structure G, how many complete mappings of G there are. In this paper we investigate a somewhat different problem. That is, how difficult it is to count the number of complete mappings of G. We show that for a closed structure, the counting problem is #P-complete. For a closed structure with a left-identity and left-cancellation law, the counting problem is also #P-complete. For an abelian group, on the other hand, the counting problem is beyond the #P-class. Furthermore, the famous counting problems of n-queen and toroidal n-queen problems are both beyond the #P-class.},
doi = {http://dx.doi.org/10.1016/S0012-365X(03)00176-6},
issn = {0012-365X},
keywords = {n-Queen problem},
number = {1â3},
url = {http://www.sciencedirect.com/science/article/pii/S0012365X03001766},
volume = {277},
}