# Representation Theorem for Multivariable Totally Symmetric Functions

@inproceedings{Chen2022RepresentationTF, title={Representation Theorem for Multivariable Totally Symmetric Functions}, author={Chongyao Chen and Ziang Chen and Jian Lu}, year={2022} }

In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric polynomials. We then study the singularity and geometry of the generators, and show that the regularity may become worse after applying the decomposition.

## References

SHOWING 1-10 OF 10 REFERENCES

### When is the algebra of multisymmetric polynomials generated by the elementary multisymmetric polynomials

- Mathematics
- 2004

Multisymmetric polynomials are the r-fold diagonal invariants of the symmetric group Sn. Elementary multisymmetric polynomials are analogues of the elementary symmetric polynomials, in the…

### Universal approximation of symmetric and anti-symmetric functions

- Computer Science, MathematicsCommunications in Mathematical Sciences
- 2022

We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We…

### Geometry of backflow transformation ansatz for quantum many-body fermionic wavefunctions

- Mathematics, Computer Science
- 2021

The geometric aspects of wave function ansatz are studied and it is shown that in general totally antisymmetric polynomials cannot be efficiently represented by backflow transformation ansatz at least in the category of polynomers.

### Tensor product expansions for correlation in quantum many-body systems

- Physics
- 1998

We explore a class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely…

### On the Limitations of Representing Functions on Sets

- Mathematics, Computer ScienceICML
- 2019

It is proved that an implementation of this model via continuous mappings (as provided by e.g. neural networks or Gaussian processes) actually imposes a constraint on the dimensionality of the latent space.

### Classical Many-Body Time Crystals.

- Physics, Computer SciencePhysical review letters
- 2019

This work provides a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators and presents a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition.

### Many-Body Theory Exposed!: Propagator Description of Quantum Mechanics in Many-Body Systems

- Physics
- 2005

Identical Particles Second Quantization Independent-Particle Model for Fermions in Finite Systems Two-Particle States and Interactions Noninteracting Bosons and Fermions Propagators in One-Particle…

### Deep sets, Advances in neural information processing systems 30 (2017)

- Email address: ziang@math.duke.edu (JL) Departments of Mathematics,
- 2017

### On representing (anti) symmetric functions, arXiv preprint arXiv:2007.15298 (2020)

- 2020