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Also 1-D are Mono-dimensional Chess by Luiz Carlos Campos, who developed Ramayana to be continued, and String Chess by Aaron Hall.
One-dimensionals are here, or linked, or in comment.
Of course, another one dimensional chess is simply the mapping from the 2D board of FIDE chess to a 1D board. You need to add separators and a rule that a knight must jump over at least one separator when moving.
This was done once, although offhand I can remember neither the name nor the inventor.
Now that I've had more time, I've found it. It's EEEEEEEEEEEEEEEEEEEEEEEX! Chess.
In the comment Black points out 2-D maps to 1-D, 3-D to 2-D, by separators, http://www.chessvariants.org/index/displaycomment.php?commentid=25177.
'knight must jump over at least one separator when moving' - it's not only separator limitation of FIDE chess on 1D board. Knight must jump over exactly 1 sparator to leap 10 squares and over exactly 2 to leap 17 squares. Bishop is (9) and (7) rider, but with each of it's leaps it must jump over exactly 1 separator. Rook can't cross separators when moves as rook, but it can move freely as (8) rider. And here are rules for new game: what if separators are ignored?! :D
That is an idea. Make a variant mapping 2D to 1D but remove and ignore the separators. And then change other rules if needed, including board setup, if that would improve the game.
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