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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Euler’s “De Partitio Numerorum”
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  • H. L. Alder, Partition identities—from Euler to the present, Amer. Math. Monthly 76 (1969), 733–746. MR 263766, DOI 10.2307/2317861
  • Krishnaswami Alladi, The method of weighted words and applications to partitions, Number theory (Paris, 1992–1993) London Math. Soc. Lecture Note Ser., vol. 215, Cambridge Univ. Press, Cambridge, 1995, pp. 1–36. MR 1345170, DOI 10.1017/CBO9780511661990.002
  • George E. Andrews, On $q$-difference equations for certain well-poised basic hypergeometric series, Quart. J. Math. Oxford Ser. (2) 19 (1968), 433–447. MR 237831, DOI 10.1093/qmath/19.1.433
  • George E. Andrews, Partition identities, Advances in Math. 9 (1972), 10–51. MR 306105, DOI 10.1016/0001-8708(72)90028-X
  • George E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. MR 0557013
  • George E. Andrews, The hard-hexagon model and Rogers-Ramanujan type identities, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 9, 5290–5292. MR 629656, DOI 10.1073/pnas.78.9.5290
  • George E. Andrews, L. J. Rogers and the Rogers-Ramanujan identities, Math. Chronicle 11 (1982), no. 1-2, 1–15. MR 677447
  • George E. Andrews, Euler’s pentagonal number theorem, Math. Mag. 56 (1983), no. 5, 279–284. MR 720648, DOI 10.2307/2690367
  • George E. Andrews, Generalized Frobenius partitions, Mem. Amer. Math. Soc. 49 (1984), no. 301, iv+44. MR 743546, DOI 10.1090/memo/0301
  • GEA10 G. E. Andrews, Partitions, from The History of Combinatorics, R. Wilson, ed., to appear.
  • George E. Andrews and R. J. Baxter, Lattice gas generalization of the hard hexagon model. III. $q$-trinomial coefficients, J. Statist. Phys. 47 (1987), no. 3-4, 297–330. MR 894396, DOI 10.1007/BF01007513
  • George E. Andrews, R. J. Baxter, and P. J. Forrester, Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities, J. Statist. Phys. 35 (1984), no. 3-4, 193–266. MR 748075, DOI 10.1007/BF01014383
  • F. C. Auluck, On some new types of partitions associated with generalized Ferrers graphs, Proc. Cambridge Philos. Soc. 47 (1951), 679–686. MR 45147, DOI 10.1017/S0305004100027134
  • Richard E. Borcherds, Automorphic forms on $\textrm {O}_{s+2,2}(\textbf {R})$ and infinite products, Invent. Math. 120 (1995), no. 1, 161–213. MR 1323986, DOI 10.1007/BF01241126
  • A. Cayley, Note on a Partition-Series, Amer. J. Math. 6 (1883/84), no. 1-4, 63–64. MR 1505342, DOI 10.2307/2369210
  • Leonard Eugene Dickson, History of the theory of numbers. Vol. I: Divisibility and primality. , Chelsea Publishing Co., New York, 1966. MR 0245499
  • Leonhard Euler, Introduction to analysis of the infinite. Book I, Springer-Verlag, New York, 1988. Translated from the Latin and with an introduction by John D. Blanton. MR 961255, DOI 10.1007/978-1-4612-1021-4
  • Euler17 L. Euler, Evolutis producti infiniti $(1-x)(1-xx)(1-x^3)(1-x^4)(1-x^5)(1-x^6)$ etc., Opera Omnia (1) 3, 472–479.
  • Nathan J. Fine, Basic hypergeometric series and applications, Mathematical Surveys and Monographs, vol. 27, American Mathematical Society, Providence, RI, 1988. With a foreword by George E. Andrews. MR 956465, DOI 10.1090/surv/027
  • Gollnitz H. Göllnitz, Einfache Partitionen, Diplomarbeit W. S., 1960, Göttingen, 65 pp.
  • Basil Gordon, Some continued fractions of the Rogers-Ramanujan type, Duke Math. J. 32 (1965), 741–748. MR 184001
  • G. H. Hardy, Ramanujan. Twelve lectures on subjects suggested by his life and work, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1940. MR 0004860
  • G. H. Hardy, Collected papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others). Vol. I, Clarendon Press, Oxford, 1966. Edited by a committee appointed by the London Mathematical Society. MR 0201267
  • G. H. Hardy, Collected papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others). Vol. I, Clarendon Press, Oxford, 1966. Edited by a committee appointed by the London Mathematical Society. MR 0201267
  • G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
  • C. G. J. Jacobi, Gesammelte Werke. Bände I–VIII, Chelsea Publishing Co., New York, 1969 (German). Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften. Zweite Ausgabe. MR 0260557
  • Percy A. MacMahon, Combinatory analysis, Chelsea Publishing Co., New York, 1960. Two volumes (bound as one). MR 0141605
  • Ken Ono, Distribution of the partition function modulo $m$, Ann. of Math. (2) 151 (2000), no. 1, 293–307. MR 1745012, DOI 10.2307/121118
  • Ken Ono, The web of modularity: arithmetic of the coefficients of modular forms and $q$-series, CBMS Regional Conference Series in Mathematics, vol. 102, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2004. MR 2020489
  • Rogers1 L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc., 25 (1894), 318–343. Rogers2 L. J. Rogers, On two theorems of combinatory analysis and some allied identities, Proc. London Math. Soc. (2), 16 (1917), 315–336. RogersRam L. J. Rogers and S. Ramanujan, Proof of certain identities in combinatory analysis (with a prefatory note by G. H. Hardy), Proc. Cambridge Phil. Soc., 19 (1919), 211–216. Schur I. Schur, Ein Beitrag zur additiven zahlentheorie und zur Theorie der Kettenbrüche, Sitz. Preuss. Akad. Wiss. Phys.-Math. Kl., 1917, pp. 302–321.
  • Jean-Pierre Serre, Divisibilité de certaines fonctions arithmétiques, Enseign. Math. (2) 22 (1976), no. 3-4, 227–260. MR 434996
  • L. J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952), 147–167. MR 49225, DOI 10.1112/plms/s2-54.2.147
  • Sylvester J. J. Sylvester, Preuve graphique du theorème d’Euler sur la partition des nombres pentagonaux, Comptes Rendus, XCVI (1883), 743–745 (Reprinted: Coll. Math. Papers, Vol. 4, Cambridge University Press, Cambridge, 1912, pp. 93–94).
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Additional Information
  • George E. Andrews
  • Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 26060
  • Email:
  • Received by editor(s): April 24, 2007
  • Published electronically: June 18, 2007
  • Additional Notes: The author was partially supported by National Science Foundation Grant DMS 0200097
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 44 (2007), 561-573
  • MSC (2000): Primary 11P81, 11P83, 05A17, 05A19
  • DOI:
  • MathSciNet review: 2338365