Partitions of Integers

Abstract

The concept of partition of integers belongs to number theory as well as to combinatorial analysis. This theory was established at the end of the 18-th century by Euler. (A detailed account of the results up to ca. 1900 is found in [*Dickson, II, 1919], pp. 101–64.) Its importance was enhanced by [Hardy, Ramanujan, 1918] and [Rademacher, 1937a, b, 1938, 1940, 1943] giving rise to generalizations, which have not been exhausted yet. We will treat here only a few elementary (combinatorial and algebraical) aspects. For further reading we refer to [*Hardy, Wright, 1965], [*MacMahon, 1915–16], [Andrews, 1970, 1972b], [*Andrews, 1971], [Gupta, 1970], [Sylvester, 1884, 1886] (or Collected Mathematical Papers, Vol. 4, 1–83), and, for the beautiful asymptotic problems, to [*Ayoub, 1963] and [*Ostmann, 1956]. We use mostly the notations of the tables of [*Gupta, 1962], which are the most extensive ones on this matter.