Geodesic
A Poset Classifying Non-Commutative Term Orders
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) (2001).

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We study a poset $\Re$ on the free monoid (X*) on a countable alphabet X.This poset is determined by the fact that its total extensions are precisely the standard term orders on X*. We also investigate the poset classifying degree-compatible standard term orders, and the poset classifying sorted term orders. For the latter poset, we give a Galois coconnection with the Young lattice. 
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     author = {Snellman, Jan},
     title = {A {Poset} {Classifying} {Non-Commutative} {Term} {Orders}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)},
     year = {2001},
     doi = {10.46298/dmtcs.2286},
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Snellman, Jan. A Poset Classifying Non-Commutative Term Orders. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) (2001). doi : 10.46298/dmtcs.2286. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2286/

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