The Uzawa equivalence theorem [H. Uzawa, Walras’s Existence Theorem and Brouwer’s Fixed Point Theorem, Economic Studies Quarterly 8 (1962) 59–62] showed (classically) that the existence of Walrasian equilibrium in an economy with continuous excess demand functions is equivalent to Brouwer’s fixed point theorem, that is, the existence of a fixed point for any continuous function from an n-dimens...

In this paper, we establish an asymptotic existence theorem for group divisible designs of type mn with block sizes in any given set K of integers greater than 1. As consequences, we will prove an asymptotic existence theorem for frames and derive a partial asymptotic existence theorem for resolvable group divisible designs. © 2006 Elsevier Inc. All rights reserved.