A164361 - OEIS

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A164361

The number of elements in S_5\det^{-1}(n)/GL(5,\Z), where we take det : M_{5 \x 5}(\Z) \rightarrow \Z.

1, 4, 10, 29, 32, 89, 78, 236, 233, 381, 302, 1054, 518, 1109, 1377, 2350, 1274, 3649, 1872, 5280 (list; graph; refs; listen; history; internal format)

	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 counts 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	`A162158 and A162159 are the relative sequences in dimensions 3 and 4 respectively.` `Sequence in context: A061639 A008995 A111236 * A006907 A052946 A026152` `Adjacent sequences: A164358 A164359 A164360 * A164362 A164363 A164364`
	KEYWORD	`nonn`
	AUTHOR	`Atanas Atanasov (ava2102(AT)columbia.edu), Aug 14 2009`

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Last modified February 15 05:45 EST 2012. Contains 205694 sequences.