## 9 Citations

Fourier Inversion for Finite Inverse Semigroups

- MathematicsSIAM J. Discret. Math.
- 2015

This paper introduces four inverse semigroup generalizations of the Fourier inversion theorem for finite groups, and describes a general approach to the construction of fast inverse Fourier transforms for finite inverse semigroups complementary to an approach to FFTs given in previous work.

The Efficient Computation of Fourier Transforms on Semisimple Algebras

- Mathematics
- 2016

We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best…

Approximating monoid actions by group actions.

- Mathematics
- 2016

Let $M$ be a monoid. We construct a family of model structures on the category of $M$-spaces. The weak equivalences of these model categories are defined by using the universally assigned groups…

Simplicity of Augmentation Submodules for Transformation Monoids

- MathematicsAlgebras and Representation Theory
- 2020

For finite permutation groups, simplicity of the augmentation submodule is equivalent to 2-transitivity over the field of complex numbers. We note that this is not the case for transformation…

The Global Dimension of the full Transformation Monoid (with an Appendix by V. Mazorchuk and B. Steinberg)

- Mathematics
- 2015

The representation theory of the symmetric group has been intensively studied for over 100 years and is one of the gems of modern mathematics. The full transformation monoid 𝔗n$\mathfrak {T}_{n}$…

Homotopical categories of spaces with monoid actions

- Mathematics
- 2016

Let $M$ be a monoid. We construct a family of homotopical category structures on the category of $M$-spaces. Moreover, we show that each of these homotopical categories is a Brown's category of…

Signal Processing on the Permutahedron: Tight Spectral Frames for Ranked Data Analysis

- Computer ScienceArXiv
- 2021

Ranked data sets, where m judges/voters specify a preference ranking of n objects/candidates, are increasingly prevalent in contexts such as political elections, computer vision, recommender systems,…

A pr 2 01 5 THE GLOBAL DIMENSION OF THE FULL TRANSFORMATION MONOID

- 2015

## References

SHOWING 1-10 OF 27 REFERENCES

The characters of the symmetric inverse semigroup

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1957

There are two natural analogues of the symmetric group on n symbols in the theory of semigroups, namely, the set of all mappings of a set of n symbols into itself, and the set of all partial…

Möbius functions and semigroup representation theory II: Character formulas and multiplicities

- Mathematics
- 2006

Fast Fourier transforms for the rook monoid

- Mathematics
- 2009

We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divide-and-conquer algorithms (fast Fourier transforms, or…

A natural partial order for semigroups

- Mathematics
- 1986

A partial order on a semigroup (S, ) is called natural if it is defined by means of the multiplication of S. It is shown that for any semigroup (S, ) the relation a < b iff a = xb = by, xa = a for…

Matrix representations of semigroups

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1957

In a previous paper, the author gave necessary and sufficient conditions for the algebra of a finite semigroup S over a field of suitable characteristic to be semisimple. When this algebra is…

A Generalization of Spectral Analysis with Application to Ranked Data

- Mathematics
- 1989

An analog of the spectral analysis of time series is developed for data in general spaces. This is applied to data from an election in which 5738 people rank ordered five candidates. Group theoretic…

The Representation Type of the Full Transforamtion Semigroup T4

- Mathematics
- 2000

T n be the semigroup of all transformations of a set of n elements and k a field of characteristic 0. According to Ponizovskii, the semigroup algebra kTn is of finite representation type if n≤ 3.…

The algebraic theory of semigroups

- Mathematics
- 1964

This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into…

The efficient computation of Fourier transforms on the symmetric group

- MathematicsMath. Comput.
- 1998

This paper replaces the matrix multiplications in Clausen's algorithm with sums indexed by combinatorial objects that generalize Young tableaux, and writes the result in a form similar to Horner's rule.