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A162159 The number of elements in S_4\det^{-1}(n)/GL(4,\Z), where we take det : M_{4 \x 4}(\Z) \rightarrow \Z. 3
1, 3, 7, 16, 18, 37, 36, 83, 85, 116, 101, 262, 154, 264, 337, 476, 305, 657, 409, 894, 788, 851, 682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Consider the set of 4 x 4 matrices with integer entries of a fixed determinant n. The group GL(4, \Z) acts on the right by multiplication. Similarly, the symmetric group S_4 acts on the left via multiplication by permutation matrices. The entry a_n is the number of elements in the double orbit space S_4\det^{-1}(n)/GL(4,\Z). The sequence a_n also gives the number of isomorphism classes of simplicial cones in \Z^4 of a certain index, or alternatively the number of affine toric varieties in dimension 4 arising from simplicial cones.

LINKS

Atanas Atanasov, Table of n, a(n) for n=1..50

EXAMPLE

For n = 2, three representatives are [4,4]((1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,1,2)), ((1,0,0,0),(0,1,0,0),(0,0,1,0),(0,1,1,2)) and ((1,0,0,0),(0,1,0,0),(0,0,1,0),(1,1,1,2)).

CROSSREFS

A162158 is the relevant sequence in dimension 3.

Sequence in context: A060092 A035283 A184863 * A190890 A116040 A218276

Adjacent sequences:  A162156 A162157 A162158 * A162160 A162161 A162162

KEYWORD

nonn

AUTHOR

Atanas Atanasov (ava2102(AT)columbia.edu), Jun 26 2009

STATUS

approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)