English

A q-queens problem. VII. Combinatorial types of nonattacking chess riders

Combinatorics 2021-06-21 v2

Abstract

On a convex polygonal chessboard, the number of combinatorial types of nonattacking configuration of three identical chess riders with rr moves, such as queens, bishops, or nightriders, equals r(r2+3r1)/3r(r^2+3r-1)/3, as conjectured by Chaiken, Hanusa, and Zaslavsky (2019). Similarly, for any number of identical 3-move riders the number of combinatorial types is independent of the actual moves.

Cite

@article{arxiv.1906.08981,
  title  = {A q-queens problem. VII. Combinatorial types of nonattacking chess riders},
  author = {Christopher R. H. Hanusa and Thomas Zaslavsky},
  journal= {arXiv preprint arXiv:1906.08981},
  year   = {2021}
}

Comments

6 pp., 2 figures; v2 9 pp., 3 figures

R2 v1 2026-06-23T09:59:40.310Z