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

• Main Author: Ballantine, Cristina
• Other Authors: Department of Mathematics and Computer Science (College of the Holy Cross), College of the Holy Cross, Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2011
• Subjects: Schur functions; Vandermonde determinant; Young diagrams; symmetric functions; quantum Hall effect; [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]; [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; Gauche; Iceland
• Online Access: https://hal.inria.fr/hal-01215094; https://hal.inria.fr/hal-01215094/document; https://hal.inria.fr/hal-01215094/file/dmAO0109.pdf

International audience 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 gi...