Geodesic
All the shuffle-compatible graded orderings of 0-1-words
Séminaire lotharingien de combinatoire, Tome 10 (1984)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We show that up to (4 times) symmetry - left -> right and 0 -> 1 - the only shuffle-compatible graded orderings on words over {0,1} are those given by three concrete rules. 
@article{SLC_1984_10_a18,
     author = {Klaus Leeb and Giuseppe Pirillo},
     title = {All the shuffle-compatible graded orderings of 0-1-words},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {10},
     year = {1984},
     url = {http://geodesic.mathdoc.fr/item/SLC_1984_10_a18/}
}
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Klaus Leeb; Giuseppe Pirillo. All the shuffle-compatible graded orderings of 0-1-words. Séminaire lotharingien de combinatoire, Tome 10 (1984). http://geodesic.mathdoc.fr/item/SLC_1984_10_a18/