@article{Team_2020, title={Some Forbidden Rectangular Chessboards with Generalized Knight’s Moves: Sirirat Singhun, Krit Karudilok, Ratinan Boonklurb}, url={https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/960}, abstractNote={<div> <p>The m × n chessboard is an array with squares arranged in m rows and n columns. An (a,b)-knight’s move or generalized knight’s move is a move from one square to another by moving a knight passing a squares vertically or asquares horizontally and then passing b squares at 90 degrees angle. A closed (a, b)-knight’s tour is an (a, b)-knight’s move such that the knight lands on every square on the m × n chessboard once and returns to its starting square. In this paper, we show that (i) the (a + b) × n chessboard admits no closed (a, b)-knight’s tours if n ∈ [2b + 1, 4b − 1] where 1 ≤ a &lt; b or if n ∈ [4b + 1, 5b] where 1 ≤ a &lt; b &lt; 2a, and (ii) the (2a + 1) × n chessboard admits no closed (a, a + 1)-knight’s tours if n = 4a+4 where a ≥ 1, or if n = 6a+6 where a &gt; 3, or if n = 6a+8 where a &gt; 3.</p> </div>}, journal={Thai Journal of Mathematics}, author={Team, Support}, year={2020}, month={Mar.}, pages={133–145} }