A $q$-Queens Problem. V. Some of Our Favorite Pieces: Queens, Bishops, Rooks, and Nightriders

@article{Chaiken2016AP,
  title={A \$q\$-Queens Problem. V. Some of Our Favorite Pieces: Queens, Bishops, Rooks, and Nightriders},
  author={Seth Chaiken and Christopher R. H. Hanusa and Thomas Zaslavsky},
  journal={arXiv: Combinatorics},
  year={2016}
}
Parts I-IV showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function of $n$ whose coefficients are essentially polynomials in $q$. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds… 

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