Sequences in overpartitions
Tóm tắt
This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these ends.
Tài liệu tham khảo
Ablinger, J., Uncu, A.K.: qFunctions—a mathematica package for \(q\)-series and partition theory applications. J. Symb. Comput. 107, 145–166 (2021)
Andrews, G.E.: The Theory of Partitions, Cambridge Mathematical Library, Cambridge University Press, Cambridge (1998). Reprint of the original. MR1634067 (99c:11126) (1976)
Andrews, G.E.: Partitions with short sequences and mock theta functions. Proc. Nat. Acad. Sci. 102(13), 4666–4671 (2005)
Andrews, G.E.: Sequences in Partitions, Double \(q\)-Series, and the Mock Theta Functions \(\rho _3(q)\), from Algorithmic Combinatorics-Enumerative Combinatorics, Special Functions and Computer Algebra, pp. 25–46. Springer, Cham (2020)
Andrews, G.E., Berndt, B.C., Jacobsen, L., Lampede, R.L.: The continued fractions found in the unorganized portions of Ramanujan’s notebooks. Mem. Am. Math. Soc. 99(477) (1992)
Andrews, G.E., Berndt, B.C., Sohn, J., Yee, A.J., Zaharescu, A.: On Ramanujan’s continued fraction for \((q^2;q^3)_\infty /(q;q^3)_\infty \). Trans. Am. Math. Soc. 355(6):2397–2411 (2003)
Bringmann, K., Mahlburg, K., Nataraj, K.: Distinct parts partitions without sequences. Elec. J. Comb. 22 (2015)
Choi, Y., Kim, B., Lovejoy, J.: Overpartitions into distinct parts without short sequences. J. Num. Theo. 175, 117–133 (2017)
Gasper, G., Rahman, M.: Basic Hypergeometric Series. Cambridge University Press, Cambridge (2004)
Hirschhorn, M.D.: Developments in the theory of partitions, Ph.D. Thesis. University of New South Wales (1980)
Holroyd, A.E., Liggett, T.M., Romik, D.: Integrals, partitions, and cellular automata. Trans. Am. Math. Soc. 356, 3349–3368 (2004)
Kauers, M., Koutschan, C.: A mathematica package for q-holonomic sequences and power series. Ramanujan J 19(2), 137–150 (2009)
Koutschan, C.: Advanced Applications of the Holonomic Systems Approach, RISC, Johannes Kepler University, Linz. PhD Thesis. September (2009)
MacMahon, P.A.: Combinatory Analysis, vol. 2. Cambridge University Press, Cambridge (1918) (Reprinted: Chelsea/AMS, Providence, 2001)
Sylvester, J.J.: A constructive theory of partitions, arranged in three acts, an interaction and exodition. Am. J. Math. 5 (1882) pp. 251–330 and 6 (184), pp. 334–336 (1882–1884) (or pp. 1–83 of The Collected Mathematical Papers of J. J. Sylvester, Vol. 4. 12; reprinted by Chelsea, New York, 1974)