Author

Yi-Xiang Kong

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Preprint Sep 2026

Orthodox queen domination: finite constructions and an asymptotic density gap

An orthodox dominating set on an $n\times n$ chessboard occupies every row of one parity and every column of a possibly different parity. For $n\ge400001$, every such set contains more than $(1/2+1/80000)n-2$ queens, on odd and even boards and with attacking or boundary queens allowed. Second-moment estimates and an ex...

Yi-Xiang Kong · 0 citations

Preprint Aug 2026

An Explicit 82-Queen Covering of the 163 x 163 Board and Its Asymptotic Implication

The queen's graph $Q_n$ has the squares of the $n\times n$ chessboard as vertices, with adjacency defined by a common row, column, or diagonal. We give an explicit set of $82$ queens on $Q_{163}$. In centered coordinates, all queen coordinates are odd, every odd row and odd column is occupied exactly once, and the occu...

Yi-Xiang Kong · 0 citations