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A retrievel of a Sperner map from a Sperner matroid is illustrated. As an application, a new proof of a completion theorem of Lovász's matroid version of Sperner's lemma is given.
Combinatorics of complexes plays an important role in topology, nonlinear analysis, game theory, and mathematical economics. In 1967, Ky Fan used door-to-door principle to prove a combinatorial Stokes' theorem on pseudomanifolds. In 1993, Shih and Lee developed the geometric context of general position maps, π-balanced and π-subbalanced sets and used them… (More)