# 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…

## 4 Citations

### A q-queens problem III. Nonattacking partial queens

- MathematicsAustralas. J Comb.
- 2019

For three nonattacking partial queens, the unified framework presented here for partial queens allows us to explicitly compute the four highest-order coefficients of the counting quasipolynomial, show that the five highest- order coefficients are constant (independent of $n), and find the period of the next coefficient.

### A q-Queens Problem IV. Attacking configurations and their denominators

- MathematicsDiscret. Math.
- 2020

### A Plethora of Polynomials: A Toolbox for Counting Problems

- Mathematics, Computer ScienceAm. Math. Mon.
- 2022

A tour through numerous problems in combinatorics and discrete optimization that depend on counting the set S of integer points in a polytope, or in some more general object constructed via discrete geometry and first-order logic, and considers families of such sets St depending on one or more integer parameters t.

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