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Search: id:A127709
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| A127709 |
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Table T(d,n) = the number of isomorphism classes of smooth Fano d-polytopes with n vertices, read by rows. |
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1
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| 1, 1, 2, 1, 1, 4, 1, 1, 7, 9, 1, 4, 28, 15, 1, 2, 47, 91, 26, 1, 27, 268, 257, 40, 10, 312, 1318, 643, 1, 137, 2807, 5347, 1, 35, 2204, 19516, 5, 771, 26312, 2, 186, 14758, 39, 4362, 11, 1013, 1, 214, 1, 43, 5, 2
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Abstract: "We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes." The column sums make a good sequence, too.
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LINKS
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Mikkel Obro, An algorithm for the classification of smooth Fano polytopes, Apr 02 2007, p. 15.
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EXAMPLE
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Table begins:
n..|d=1|d=2|d=3|d=4|d=5|d=6|d=7
1..|...........................
2..|.1.|.......................
3..|...|.1.|...................
4..|...|.2.|.1.|...............
5..|...|.1.|.4.|.1.|...........
6..|...|.1.|.7.|.9.|.1.|.......
7..|...|...|.4.|.28|.15|.1.|...
8..|...|...|.2.|.47|.91|.26|.1.
9..|...|...|...|.27|268|257|.40
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CROSSREFS
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Adjacent sequences: A127706 A127707 A127708 this_sequence A127710 A127711 A127712
Sequence in context: A122578 A005131 A105477 this_sequence A131350 A131087 A105475
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KEYWORD
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nonn,tabl
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Apr 03 2007
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