Number of open and closed rook's tours

Asked Feb 03 '19 at 16:46

Active Feb 03 '19 at 18:04

Viewed 99 times

Knight's tour is very well known problem, but what about rook's tour? On $n\times1$ chessboard there are obviously $n!$ open and $(n-1)!$ closed tours.

Is there a way to easily compute number of open and closed rook's tours on $n\times m$ (or just for some small $m$) chessboard? Question doesn't look trivial, so I don't know what can be added to make it more informative. I will appreciate any references.

edited Feb 03 '19 at 18:04

asked Feb 03 '19 at 16:46

user514787

1,475

1

See A096121 for $n\times2$ and A096970 for $n\times n$. – bof Feb 04 '19 at 00:51
1

Forgot to mention, those references are for open tours. I didn't see anything on closed tours. – bof Feb 04 '19 at 00:59
@bof, thank you very much! – user514787 Feb 04 '19 at 12:59
@bof, can you please also (if you have time) look for a proof of $n\times2$? – user514787 Feb 08 '19 at 16:37
Now the last thing is asked here. – metamorphy Mar 10 '21 at 05:26

Number of open and closed rook's tours

0 Answers0