About the Project



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1: 26.1 Special Notation
Many combinatorics references use the rising and falling factorials: …
2: 26.19 Mathematical Applications
§26.19 Mathematical Applications
Combinatorics has applications to analysis, algebra, and geometry. …Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). …
3: 26.20 Physical Applications
§26.20 Physical Applications
An English translation of Pólya (1937) on applications of combinatorics to chemistry has been published as Pólya and Read (1987). …The latter reference also describes chemical applications of other combinatorial techniques. Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). For an application of statistical mechanics to combinatorics, see Bressoud (1999). …
4: Ira Gessel
Gessel has published numerous papers in enumerative combinatorics. …
5: 26.22 Software
  • RISC Combinatorics Group (website).

  • World Combinatorics Exchange (website).

  • 6: Peter Paule
    Paule’s main research interests are computer algebra and algorithmic mathematics, together with connections to combinatorics, special functions, number theory, and other related fields. He is on the editorial boards for the Journal of Symbolic Computation and The Ramanujan Journal, and is Managing Editor of Annals of Combinatorics. …
    7: 15.17 Mathematical Applications
    §15.17(iv) Combinatorics
    In combinatorics, hypergeometric identities classify single sums of products of binomial coefficients. …
    8: Mourad E. H. Ismail
    Ismail has published numerous papers on special functions, orthogonal polynomials, approximation theory, combinatorics, asymptotics, and related topics. …  Suslov), Kluwer Academic Publishers, 2001; Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (with F. …
    9: 32.14 Combinatorics
    §32.14 Combinatorics
    10: 16.23 Mathematical Applications
    §16.23(iv) Combinatorics and Number Theory