Variable-Dimension Complexes with Applications.

Abstract
In the past few years, researchers in fixed-point methods have developed a number of variable-dimension simplicial algorithms. These algorithms are shown to be specific realizations of pivoting methods on a V-complex. The concept of a V-complex is also used to give new and constructive proofs of a variety of known theorems in combinatorial topology and mathematical programming. Finally, V-complexes give rise to new theorems in complementarity theory and combinatorial topology, including a generalization of the Sperner Lemma, a covering theorem on the the simplex, and a new combinatorial lemma on the n-cube. (Author)

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