133 citations · 1.4k across the 77 of their papers we have counts for
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Schur Partial Derivative Operators
Jean-Christophe Aval, Nantel Bergeron
A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice cells. The corresponding lattice diagram determinant is Δ_L(X;Y)=\det \| x_i^{p_j}y_i^{q_j} \|. These latti…
Catalan paths, Quasi-symmetric functions and Super-Harmonic Spaces
Jean-Christophe Aval, Nantel Bergeron
We investigate the quotient ring of the ring of formal power series $\Q[[x_1,x_2,...]]$ over the closure of the ideal generated by non-constant quasi-\break symmetric functions…
Vanishing ideals of Lattice Diagram determinants
J. -C. Aval, N. Bergeron
A lattice diagram is a finite set of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is $Δ_L(\X;\Y)=\det \| x…
q and q,t-Analogs of Non-commutative Symmetric Functions
Nantel Bergeron, Mike Zabrocki
We introduce two families of non-commutative symmetric functions that have analogous properties to the Hall-Littlewood and Macdonald symmetric functions.
Lattice Diagram polynomials in one set of variables
Jean-Christophe Aval, Francois Bergeron, Nantel Bergeron
The space spanned by all partial derivatives of the lattice polynomial is investigated in math.CO/9809126 and many conjectures are given. Here, we prov…