Skip to Main content Skip to Navigation
Conference papers

Powers of the Vandermonde determinant, Schur functions, and the dimension game

Abstract : Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, I will give a recursive approach for computing the coefficient of the Schur function $s_μ$ in the decomposition of an even power of the Vandermonde determinant in $n+1$ variables in terms of the coefficient of the Schur function $s_λ$ in the decomposition of the same even power of the Vandermonde determinant in $n$ variables if the Young diagram of $μ$ is obtained from the Young diagram of $λ$ by adding a tetris type shape to the top or to the left.
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download

https://hal.inria.fr/hal-01215094
Contributor : Coordination Episciences Iam <>
Submitted on : Tuesday, October 13, 2015 - 3:06:40 PM
Last modification on : Tuesday, August 6, 2019 - 3:24:02 PM
Long-term archiving on: : Thursday, April 27, 2017 - 12:15:12 AM

File

dmAO0109.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01215094, version 1

Collections

Citation

Cristina Ballantine. Powers of the Vandermonde determinant, Schur functions, and the dimension game. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.87-98. ⟨hal-01215094⟩

Share

Metrics

Record views

202

Files downloads

1117