Alain Lascoux
Published 2006-02-17Version 1
Eliminating the arbitrary coefficients in the equation of a generic plane curve of order $n$ by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to conics, has been obtained by Monge. Sylvester, Halphen, Cartan used invariants of higher order. The expression of these invariants is rather complicated, but becomes much simpler when interpreted in terms of symmetric functions.
Macdonald polynomials and symmetric functions
The primitives and antipode in the Hopf algebra of symmetric functions in noncommuting variables
Partitions, rooks, and symmetric functions in noncommuting variables
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