A173878 Number of six-dimensional simplical toric diagrams with hypervolume n.

1, 3, 7, 23, 19, 65, 46, 202, 156, 281, 183, 972, 333, 903, 1029, 2507, 912

Offset: 1

Author

Rak-Kyeong Seong (rak-kyeong.seong(AT)imperial.ac.uk), Mar 01 2010

Keywords

• nonn
• more

Comments

Also gives the number of distinct abelian orbifolds of C^7/Gamma, Gamma in SU(7).

Links

• Gabriele Balletti, Dataset of "small" lattice polytopes
• J. Davey, A. Hanany and R. K. Seong, Counting Orbifolds, J. High Energ. Phys. (2010) 2010: 10; arXiv:1002.3609 [hep-th], 2010.
• A. Hanany and R. K. Seong, Symmetries of abelian orbifolds, J. High Energ. Phys. (2011) 2011: 27; arXiv:1009.3017 [hep-th], 2010-2011.
• Andrey Zabolotskiy, Coweight lattice A^*_n and lattice simplices, arXiv:2003.10251 [math.CO], 2020.

Crossrefs

Cf. A003051 (No. of two-dimensional triangular toric diagrams of area n), A045790 (No. of three-dimensional tetrahedral toric diagrams of volume n), A173824 (No. of four-dimensional simplical toric diagrams of hypervolume n), A173877 (No. of five-dimensional simplical toric diagrams of hypervolume n).

Extensions

a(8)-a(16) from Balletti's data and a(17) from Table 15 of Hanany & Seong 2011 added by Andrey Zabolotskiy, Mar 13 2020