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GENERALIZED ASYMPTOTIC EULER’S RELATION FOR CERTAIN FAMILIES OF POLYTOPES

By László Major

Abstract

Abstract. According to Euler’s relation any polytope P has as many faces of even dimension as it has faces of odd dimension. As a generalization of this fact one can compare the number of faces whose dimension is congruent to i modulo m with the number of all faces of P for some positive integer m and for some 1≤i≤m. We show some classes of polytopes for which the above proportion is asymptotically equal to 1/m

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