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Motivated by Gr\"obner basis theory for finite point configurations, wedefine and study the class of "standard complexes" associated to a matroid.Standard complexes are certain subcomplexes of the independence complex thatare invariant under matroid duality. For the lexicographic term order, thestandard complexes satisfy a deletion-contraction-type recurrence. Weexplicitly determine the lexicographic standard complexes for lattice pathmatroids using classical bijective combinatorics.

Standard complexes of matroids and lattice paths