# 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}
}
• Published 3 September 2016
• Mathematics
• arXiv: Combinatorics
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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