Francois Bergeron
Published 2011-05-29Version 1
The operator nabla, introduced by Garsia and the author, plays a crucial role in many aspect of the study of diagonal harmonics. Besides giving several new formulas involving this operator, we show how one is lead to representation theoretic explanations for conjectures about the effect of this operator on Schur functions.
A combinatorial formula for the nabla operator
Remarks on the conjectures of Capparelli, Meurman, Primc and Primc
Some conjectures on $r$-graphs and equivalences
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