# Evaluation and spanning sets of confluent Vandermonde forms

@article{Sunko2022EvaluationAS, title={Evaluation and spanning sets of confluent Vandermonde forms}, author={Denis K. Sunko}, journal={Journal of Mathematical Physics}, year={2022} }

An arbitrary derivative of a Vandermonde form in N variables is given as [ n1⋯ n N], where the ith variable is differentiated N − n i − 1 times, 1 ≤ n i ≤ N − 1. A simple decoding table is introduced to evaluate it by inspection. The special cases where 0 ≤ n i+1 − n i ≤ 1 for 0 < i < N are in one-to-one correspondence with ribbon Young diagrams. The respective N! standard ribbon tableaux map to a complete graded basis in the space of S N-harmonic polynomials. The mapping is realized as an…

## References

SHOWING 1-10 OF 13 REFERENCES

### Combinatorics, symmetric functions, and Hilbert schemes

- Mathematics
- 2002

We survey the proof of a series of conjectures in combinatorics using new results on the geometry of Hilbert schemes. The combinatorial results include the positivity conjecture for Macdonald’s…

### Entropy of pure states: not all wave functions are born equal

- Physics4open
- 2022

Many-body Hilbert space has the algebraic structure of a finitely generated free module. All N-body wave functions in d dimensions can be generated by a finite number of N!d − 1 of generators called…

### Many-Fermion Wave Functions: Structure and Examples

- Physics
- 2020

Many-fermion Hilbert space has the algebraic structure of a free module generated by a finite number of antisymmetric functions called shapes. Physically, each shape is a many-body vacuum, whose…

### Finite Unitary Reflection Groups

- MathematicsCanadian Journal of Mathematics
- 1954

Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of…

### Solution of Vandermonde Systems of Equations

- Mathematics
- 1970

We obtain in this paper a considerable improvement over a method developed earlier by Ballester and Pereyra for the solution of systems of linear equations with Vandermonde matrices of coefficients.…

### Elementary Theory: the Incompressible Quantum Fluid

- Physics
- 1990

In this lecture, I shall outline what I believe to be the correct fundamental picture of the fractional quantum Hall effect. The principal features of this picture are that the 1/3 state and its…

### Generic example of algebraic bosonisation

- Physics
- 2020

Two identical non-interacting fermions in a three-dimensional harmonic oscillator well are bosonised exactly according to a recently developed general algebraic scheme. Rotational invariance is taken…

### Natural generalization of the ground-state Slater determinant to more than one dimension

- Physics
- 2016

The basic question is addressed of how the space dimension d is encoded in the Hilbert space of N identical fermions. There appears a finite number N!