Maximum arrangements of nonattacking kings on the $2n\times 2n$ chessboard

Tricia Muldoon Brown

Maximum arrangements of nonattacking kings on the $2n\times 2n$ chessboard

Combinatorics 2022-01-19 v2

Authors: Tricia Muldoon Brown

Abstract

To count the number of maximum independent arrangements of $n^2$ kings on a $2n\times 2n$ chessboard, we build a $2^n \times (n+1)$ matrix whose entries are independent arrangements of $n$ kings on $2\times 2n$ rectangles. Utilizing upper and lower bound functions dependent of the entries of the matrix, we recursively construct independent solutions, and provide a straight-forward formula and algorithm.

Keywords

maximum independent arrangements nonattacking kings chessboard recursive construction combinatorial enumeration matrix method

Cite

@article{arxiv.2111.10331,
  title  = {Maximum arrangements of nonattacking kings on the $2n\times 2n$ chessboard},
  author = {Tricia Muldoon Brown},
  journal= {arXiv preprint arXiv:2111.10331},
  year   = {2022}
}

Maximum arrangements of nonattacking kings on the $2n\times 2n$ chessboard

Abstract

Keywords

Cite

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