Fast Fourier transforms for the rook monoid

DOI10.1090/S0002-9947-09-04838-7zbMath1264.65220arXiv0709.4175MaRDI QIDQ5189159

Martin E. Malandro, Daniel N. Rockmore

Publication date: 8 March 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.4175

zbMATH Keywords

fast Fourier transformsinverse semigroupsrook monoidsdivide-and-conquer algorithmsFFTspartially ranked data

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Numerical methods for discrete and fast Fourier transforms (65T50) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30) Inverse semigroups (20M18) Representation of semigroups; actions of semigroups on sets (20M30)

Related Items (8)

Quivers of monoids with basic algebras ⋮ Inverse semigroup spectral analysis for partially ranked data ⋮ Fast Fourier transforms for finite inverse semigroups ⋮ The efficient computation of Fourier transforms on semisimple algebras ⋮ Simplicity of augmentation submodules for transformation monoids ⋮ Fourier Inversion for Finite Inverse Semigroups ⋮ Unnamed Item ⋮ Character theory of monoids over an arbitrary field.

Cites Work

• Existence and efficient construction of fast Fourier transforms on supersolvable groups
• Fast Fourier transforms for finite inverse semigroups
• The representation theory of the symmetric groups
• A generalization of spectral analysis with application to ranked data
• Representations of the \(q\)-rook monoid.
• Representations of the rook monoid.
• Möbius functions and semigroup representation theory. II: Character formulas and multiplicities.
• Möbius functions and semigroup representation theory.
• Some remarks on the combinatorics of \(\mathcal{IS}_n\).
• Efficient Computation of the Fourier Transform on Finite Groups
• Fast Fourier Transforms for Symmetric Groups: Theory and Implementation
• The efficient computation of Fourier transforms on the symmetric group
• An Algorithm for the Machine Calculation of Complex Fourier Series
• Separation of variables and the computation of Fourier transforms on finite groups, I
• Matrix Representations of Completely Simple Semigroups
• A Specht module analog for the rook monoid
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