Theorem

MacMahon's Master Theorem

Combinatorics and Graph Theory

MacMahon's master theorem, in enumerative combinatorics and linear algebra, is a result Percy MacMahon discovered and published in his 1916 monograph Combinatory Analysis. It has become a standard tool for deriving binomial identities, including Dixon's identity, and MacMahon himself called it a master theorem for how readily it resolved many otherwise difficult combinatorial questions; later mathematicians including I. J. Good and Leonard Carlitz gave new proofs, and further quantum and noncommutative generalizations followed.

Facts
Classification
Statement Form
Identity or Equation 1
Proof Year
1916 1
MacMahon's Master Theorem
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Equation, Concepts
Identity, Concepts

In Branch

Source MacMahon's master theorem (Wikipedia)

Principal Result Of

Source MacMahon's master theorem (Wikipedia)

Proved By

Source MacMahon's master theorem (Wikipedia)
Sources
1. MacMahon's master theorem (Wikipedia)
  • Lead section
    In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra.
  • Principal Result Of: Percy Alexander MacMahon, Lead sentence of the article on the result
    It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis (1916).
  • In Branch: Linear Algebra, Lead sentence
    MMT) is a result in enumerative combinatorics and linear algebra.
  • Proved By: Percy Alexander MacMahon, Lead sentence, attribution
    discovered by Percy MacMahon
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