Abstract
We determine the Smith normal forms of the incidence matrices of points and projective ( r − 1 ) (r-1) -dimensional subspaces of PG ( n , q ) \operatorname {PG}(n,q) and of the incidence matrices of points and r r -dimensional affine subspaces of AG ( n , q ) \operatorname {AG}(n,q) for all n n , r r , and arbitrary prime power q q .
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