Kernels of modular inclusion maps

Abstract

Let R be a field and f2 an n-element set. For k<~n consider the R-vector space Mk with k-element subsets of [2 as basis. The inclusion map ~ :Mk ~ Mk-1 is the linear map defined on this basis through t~(A) :=/'1 + F2 + -. • + Fk, where the F~ are the (k 1 )-element subsets of A. Thus, we obtain a chain 0 ~---Mo ~ Ml . . . . . Mk-1 ~--Mk ~'--Mk+l . . . . . M… (More)
DOI: 10.1016/S0012-365X(96)00342-1

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