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The purpose of this article is to compute certain weighted sums over various subposets of the poset of isomorphism classes of finite abelian $${\ell}$$ ℓ -groups, where $${\ell}$$ ℓ is a fixed odd prime. These sums are similar to previous sums computed by Hall and Cohen-Lenstra. The computation expands upon the previous analysis of Cohen-Lenstra while also using the tools of hypergeometric...
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