Glaisher's theorem

Glaisher's theorem

In number theory, Glaisher's theorem is an identity useful to the study of integer partitions. It is named for James Whitbread Lee Glaisher.

It states that the number of partitions of an integer N into parts not divisible by d is equal to the number of partitions of the form:N=N_1+cdots+N_kwhere N_igeq N_{i+1} and N_igeq N_{i+d-1}+1,that is, partitions in which no part is repeated "d" or more times.

References

*


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • James Whitbread Lee Glaisher — (5 novembre 1848 à Lewisham (district londonien) 7 décembre 1928 à Cambridge), fils du météorologue James Glaisher  …   Wikipédia en Français

  • James Whitbread Lee Glaisher — (5 November 1848 7 December 1928) son of James Glaisher, the meteorologist, was a prolific English mathematician. Influential in his time on teaching at the University of Cambridge, he is now remembered mostly for work in number theory that… …   Wikipedia

  • List of mathematics articles (G) — NOTOC G G₂ G delta space G networks Gδ set G structure G test G127 G2 manifold G2 structure Gabor atom Gabor filter Gabor transform Gabor Wigner transform Gabow s algorithm Gabriel graph Gabriel s Horn Gain graph Gain group Galerkin method… …   Wikipedia

  • List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …   Wikipedia

  • List of partition topics — This is a list of partition topics, in the mathematical sense. Partition (disambiguation) lists meanings in other fields. In mathematics, a partition may be a partition of a set or an ordered partition of a set, or a partition of a graph, or a… …   Wikipedia

  • Factorial — n n! 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 …   Wikipedia

  • Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… …   Wikipedia

  • Edward Charles Titchmarsh — Naissance 1er juin 1899 Newbury (Berkshire) (Angleterre) Décès 18 janvier 1963 (à 63 ans) Oxford (Angleterre) Nationalité …   Wikipédia en Français

  • Louis Mordell — Louis Joel Mordell est un mathématicien américano britannique, né le 28 janvier 1888 à Philadelphie et mort le 12 mars 1972 à Cambridge. Pionnier par ses recherches en théorie des nombres, il est un spécialiste reconnu des équations… …   Wikipédia en Français

  • Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”