zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The efficient computation of Fourier transforms on the symmetric group. (English) Zbl 0902.20005
The paper describes techniques for the computation of Fourier transforms on symmetric groups and their homogeneous spaces. In particular, the matrix multiplication of Clausen’s algorithm is replaced by sums indexed by combinatorial objects that generalize Young tableaux, which are written in a form similar to Horner’s rule. The resulting algorithm computes the Fourier transform of a function on $S_n$ by ${3\over 4}n(n-1)n!$ multiplications and the same number of additions. The corresponding results for the inverse transforms and transforms on homogeneous spaces are also included.

20C40Computational methods (representations of groups)
20C30Representations of finite symmetric groups
65T50Discrete and fast Fourier transforms (numerical methods)
05E10Combinatorial aspects of representation theory
Full Text: DOI