We are interested in the following question. Let D=(d_1,d_2,...,d_r) be a partition of n where d_i> 0 and let K be a field. We say a vector v=(v_1,v_2,...,v_n) in K^n is D-partitioned if there is j, 1<= j <= r such that the only nonzero v_i's occur in positions d_1+d_2+---+d_(j-1)+1 to d_1+d_2+---+d_j. E.g. if D=(2,1,3) then (7,6,0,0,0,0) and (0,0,4,0,0,0) and (0,0,0,4,5,0) are all D-partitioned whereas (7,0,3,0,0,0) and (0,4,0,0,5,0) are not D-partitioned.
Let W be a subspace of K^n:=FullRowSpace(K,n) generated by D-partitioned vectors and let p:=NaturalHomomorphismBySubspace(V,W) be the canonical surjection. Now let B:=CanonicalBasis(Range(p)) and then call PreImagesRepresentative to the elements of B. Our question is, must these preimages in V be D-partitioned? (In a few examples, this seems to be the case. Best regards, Oeyvind Solberg. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
