OFFSET
1,2
COMMENTS
Also gives the number of distinct abelian orbifolds of C^5/Gamma, Gamma in SU(5).
LINKS
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. Table 5 gives a(1)-a(80), but the terms a(36) and a(65) there are apparently erroneous.
Andrey Zabolotskiy, Coweight lattice A^*_n and lattice simplices, arXiv:2003.10251 [math.CO], 2020.
PROG
(Sage)
# see Python in A159842 for the definition of dc, fin, per, u, N, N2
def fin_d(d):
return fin(*(d.get(n+1, 0) for n in range(max(d))))
def a(n): # see Hanany & Seong 2011, Table 1 row D=5 and Table 9
return (dc(u, N, N2, lambda n: n**3)(n) +
10 * dc(u, u, N, N2, fin(1, -1, 0, 8))(n) +
15 * dc(u, u, N, N, fin_d({1: 1, 2: -3, 4: 14, 8: -12, 16: 16}))(n) +
20 * dc(u, u, N, per(0, 1, -1), fin(1, 0, -1, 0, 0, 0, 0, 0, 9))(n) +
20 * dc(u, u, u, per(0, 1, -1), fin(1, -1, 0, 2), fin(1, 0, -1, 0, 0, 0, 0, 0, 3))(n) +
30 * dc(u, u, u, per(0, 1, 0, -1), fin_d({1: 1, 2: -2, 4: 3, 16: 6, 32: -8, 64: 8}))(n) +
24 * dc(u, per(0, 1, -1, -1, 1), per(0, 1, I, -I, -1), per(0, 1, -I, I, -1))(n)) / 120
print([a(n) for n in range(1, 100)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Rak-Kyeong Seong (rak-kyeong.seong(AT)imperial.ac.uk), Feb 25 2010
EXTENSIONS
a(16) corrected, terms a(31) and beyond added from Hanany & Seong 2011 by Andrey Zabolotskiy, Jun 30 2019
a(36) corrected from 2202 to 2215 by Andrey Zabolotskiy, Sep 20 2022
STATUS
approved