A060345
An expansion related to Yukawa coupling.
Original entry on oeis.org
5, 2875, 4876875, 8564575000, 15517926796875, 28663236110956000, 53621944306062201000, 101216230345800061125625, 192323666400003538944396875, 367299732093982242625847031250, 704288164978454714776724365580000, 1354842473951260627644461070753075500, 2613295702542192770504516764304958585000
Offset: 0
a(10) = A060041(1) + 8*A060041(2) + 125*A060041(5) + 1000*A060041(10) = 704288164978454714776724365580000.
- Gheorghe Coserea, Table of n, a(n) for n = 0..300
- P. Candelas et al., A pair of Calabi-yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991), 21-74.
- Daniel B. Grunberg and Pieter Moree, with an Appendix by Don Zagier, Sequences of enumerative geometry: congruences and asymptotics, arXiv:math/0610286 [math.NT], 2006.
- David R. Morrison, Mathematical Aspects of Mirror Symmetry, arXiv:alg-geom/9609021, 1996, see Table 1 p. 60; in Complex Algebraic Geometry (J. Kollár, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340.
-
cumsum(v) = for(i=2, #v, v[i] += v[i-1]); v;
seq(N, {d=5}) = {
my(x = 'x + O('x^(N+1)), h = cumsum(vector(d*N, n, 1/n)),
y0 = sum(n=0, N, (d*n)!/n!^d * x^n),
y1 = d * sum(n = 1, N, ((d*n)!/n!^d * (h[d*n] - h[n])) * x^n),
Qx = x * exp(y1/y0), Xq = serreverse(Qx));
Vec(d * (x * Xq'/Xq)^(d-2) / ((1 - d^d*Xq) * sqr(subst(y0, 'x, Xq))));
};
seq(20) \\ Gheorghe Coserea, Jul 29 2016
A076910
Coefficients of 5-point function in dimension 5.
Original entry on oeis.org
7, 3727381, 2637885990187, 1927092954108108787, 1425153551321014327663291, 1060347883438857662557634869906, 791661306374088776109692880989252173, 592348256908461616176898022359492565546566, 443865568545713063761643598030194801299861575595, 332947403131697202086626568381790256001850741509664373
Offset: 0
- Brian R. Greene, David R. Morrison, and M. Ronen Plesser, Mirror Manifolds in Higher Dimension, Commun. Math. Phys., 173 (1995), 559-598; arXiv:hep-th/9402119, 1994.
- David R. Morrison, Mathematical Aspects of Mirror Symmetry, in Complex Algebraic Geometry (J. Kollár, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340.
A076911
Coefficients of 6-point function in dimension 6.
Original entry on oeis.org
8, 106975232, 1672023727001600, 26611692333081695092736, 426129121674687823674948571136, 6842148599241293047857339542861643776, 110018992594692024449889564415904439556898816, 1770551943055574073245974844490813198478975912902656, 28508925683951911989843155602330000507452539542539447947264
Offset: 0
- Brian R. Greene, David R. Morrison, and M. Ronen Plesser, Mirror Manifolds in Higher Dimension, Commun. Math. Phys., 173 (1995), 559-598; arXiv:hep-th/9402119, 1994.
- David R. Morrison, Mathematical Aspects of Mirror Symmetry, in Complex Algebraic Geometry (J. Kollár, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340.
A076913
Coefficients of 3-point function in dimension 4.
Original entry on oeis.org
6, 60480, 440884080, 6255156277440, 117715791990353760, 2591176156368821985600
Offset: 0
- Geir Ellingsrud and Stein Arild Stromme, Bott's formula and enumerative geometry. J. Amer. Math. Soc. 9 (1996), 175-193. [arXiv:alg-geom/9411005]
- A. Klemm and R. Pandharipande, Enumerative geometry of Calabi-Yau 4-folds, Commun. Math. Phys., 281 (2008), 621-653; arXiv:math/0702189 [math.AG], 2007.
- David R. Morrison, Mathematical Aspects of Mirror Symmetry, in Complex Algebraic Geometry (J. Kollár, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340.
A076915
Coefficients of 3-point function in dimension 5 Y^1_2.
Original entry on oeis.org
7, 1707797, 510787745643, 222548537108926490, 113635631482486991647224
Offset: 0
- David R. Morrison, Mathematical Aspects of Mirror Symmetry, arXiv:alg-geom/9609021, 1996; in Complex Algebraic Geometry (J. Kollár, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340.
- Aleksey Zinger, Genus-Zero Two-Point Hyperplane Integrals in the Gromov-Witten Theory, Communications in Analysis and Geometry, 17 (2009), 955-999; arXiv:0705.2725 [math.AG], 2007.
Showing 1-5 of 5 results.
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