OFFSET
1,2
COMMENTS
Consider the set of 5 x 5 matrices with integer entries of a fixed determinant n. The group GL(5, \Z) acts on the right by multiplication. Similarly, the symmetric group S_5 acts on the left via multiplication by permutation matrices. The entry a_n is the number of elements in the double orbit space S_5\det^{-1}(n)/GL(5,\Z). The sequence a_n also gives the number of isomorphism classes of simplicial cones in \Z^5 of a certain index, or alternatively the number of affine toric varieties in dimension 5 arising from simplicial cones.
EXAMPLE
For n = 2, four representatives are [5,5]((1,0,0,0,0),(0,1,0,0,0),(0,0,1,0,0),(0,0,0,1,0),(0,0,0,1,2)), [5,5]((1,0,0,0,0),(0,1,0,0,0),(0,0,1,0,0),(0,0,0,1,0),(0,0,1,1,2)), [5,5]((1,0,0,0,0),(0,1,0,0,0),(0,0,1,0,0),(0,0,0,1,0),(0,1,1,1,2)), and [5,5]((1,0,0,0,0),(0,1,0,0,0),(0,0,1,0,0),(0,0,0,1,0),(1,1,1,1,2)).
CROSSREFS
KEYWORD
nonn
AUTHOR
Atanas Atanasov (ava2102(AT)columbia.edu), Aug 14 2009
STATUS
approved