Some Forbidden Rectangular Chessboards with Generalized Knight's Moves

被引：0

作者：

Singhun, Sirirat ^{[1
]}

Karudilok, Krit ^{[1
]}

Boonklurb, Ratinan ^{[2
]}

机构：

[1] Ramkhamhang Univ, Fac Sci, Dept Math, Bangkok 10240, Thailand

[2] Chulalongkorn Univ, Fac Sci, Dept Math & Comp Sci, Bangkok 10330, Thailand

来源：

THAI JOURNAL OF MATHEMATICS | 2020年

关键词：

Hamiltonian cycle; closed knight's tour; m x n chessboard; generalized knight's move; forbidden chessboard;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The m x 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 a squares 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 x n chessboard once and returns to its starting square. In this paper, we show that (i) the (a + b) x n chessboard admits no closed (a; b)-knight's tours if n is an element of 2 [2b + 1; 4b 1] where 1 <= a < b or if n is an element of [4b + 1; 5b] where 1 <= a < b < 2a, and (ii) the (2a + 1) x 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 > 3, or if n = 6a+8 where a > 3.

引用

页码：133 / 145

页数：13