# On Foulkes characters

@article{Miller2021OnFC, title={On Foulkes characters}, author={Alexander R. Miller}, journal={Mathematische Annalen}, year={2021}, volume={381}, pages={1589 - 1614} }

Orthogonality relations for Foulkes characters of full monomial groups are presented, along with three solutions to the problem of decomposing products of these characters, and new applications, including a product reformulation of a Markov chain for adding random numbers studied by Diaconis and Fulman, and a new proof of a theorem of Zagier which generalizes one of Harer and Zagier on the enumeration of Riemann surfaces of a given genus.

## 3 Citations

### The characters of symmetric groups that depend only on length

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- 2021

. The characters χ ( π ) of S n that depend only on the number of cycles of π are completely determined.

### Labeled binary trees, subarrangements of the Catalan arrangements, and Schur positivity

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## References

SHOWING 1-10 OF 20 REFERENCES

### On the distribution of the number of cycles of elements in symmetric groups

- Mathematics
- 1995

Abstract. We give a formula for the number of elements in a fixed conjugacy class of a symmetric group whose product with a cyclic permutation has a given number of cycles. A consequence is a very…

### Foulkes characters for complex reflection groups

- Mathematics
- 2015

Foulkes discovered a marvelous set of characters for the symmetric group by summing Specht modules of certain ribbon shapes according to height. These characters have many remarkable properties and…

### Carries, Combinatorics, and an Amazing Matrix

- Mathematics
- 1997

* The eigenvalues are all positive and form a finite, decreasing, geometric sequence; furthermore, if we diagonalize II as U-1IIU = D, where the eigenvalues are arranged in decreasing order in the…

### Properties and Applications of the Recurrence $F( {i + 1,k + 1,n + 1} ) = q^{k + 1} F( {i,k + 1,n} ) - q^k F( {i,k,n} )$

- Mathematics
- 1976

The above recurrence formula occurs in the algebraic theory of certain association schemes. Explicit solutions are given in terms of Gaussian binomial coefficients. In particular, some generalized…

### United States of America

- Environmental ScienceWorld Statistics Pocketbook 2011
- 2012

This section describes the contributions of the United States of America to international efforts in atmospheric chemical / dynamical and UV radiation monitoring and research relevant to global…

### Some characters that depend only on length

- Mathematics
- 2017

The author recently introduced Foulkes characters for a wide variety of reflection groups, and the hyperoctahedral ones have attracted some special attention. Diaconis and Fulman connected them to…

### Eulerian numbers, Newcomb's problem and representations of symmetric groups

- MathematicsDiscret. Math.
- 1980