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Let F be a field of characteristic p, and if Ω is an n-set let Mn be the vector space over F with basis 2Ω. We continue our investigation of modular homological Sn-representations which arise from the r-step inclusion map. This is the FSn-homomorphism ∂r:Mn→Mn which sends a k-element subset Δ⊆Ω onto the sum of all (k−r)-element subsets of Δ. Using homological methods one can give explicit character and dimension formulae.