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Number of five-dimensional simplical toric diagrams with hypervolume n.
3

%I #15 Jul 03 2020 06:22:23

%S 1,3,6,17,13,40,27,106,78,127,79,391,129,321,358,832,285,1070,409,1549

%N Number of five-dimensional simplical toric diagrams with hypervolume n.

%C Also gives the number of distinct abelian orbifolds of C^6/Gamma, Gamma in SU(6).

%H J. Davey, A. Hanany and R. K. Seong, <a href="https://doi.org/10.1007/JHEP06(2010)010">Counting Orbifolds</a>, J. High Energ. Phys. (2010) 2010: 10; <a href="https://arxiv.org/abs/1002.3609">arXiv:1002.3609 [hep-th]</a>, 2010.

%H A. Hanany and R. K. Seong, <a href="https://doi.org/10.1007/JHEP01(2011)027">Symmetries of abelian orbifolds</a>, J. High Energ. Phys. (2011) 2011: 27; <a href="https://arxiv.org/abs/1009.3017">arXiv:1009.3017 [hep-th]</a>, 2010-2011.

%H Andrey Zabolotskiy, <a href="https://arxiv.org/abs/2003.10251">Coweight lattice A^*_n and lattice simplices</a>, arXiv:2003.10251 [math.CO], 2020.

%Y 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), A173878.

%K nonn,more

%O 1,2

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

%E a(9) corrected, a(15)-a(20) added from Hanany & Seong 2011 by _Andrey Zabolotskiy_, Jun 30 2019