A Poset Classifying Non-Commutative Term Orders

Jan Snellman (1)

1 LIU - Linköping University

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.

Mots clés: term orders; free associative algebra

Domaines: Informatique [cs]; Géométrie algorithmique [cs.CG]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Interface homme-machine [cs.HC]

Jan Snellman. A Poset Classifying Non-Commutative Term Orders. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. pp.301-314, ⟨10.46298/dmtcs.2286⟩. ⟨hal-01182966⟩