Lattice Diagram polynomials in one set of variables

Details Lattice Diagram polynomials in one set of variables Lattice Diagram polynomials in one set of variables

2001-03-27

arxiv.org/abs/math/0103181v1

Adv. in Appl. Math. 28 (2002), no. 3-4, 343--359.

Mathematics

Combinatorics

15 pages

Scientific paper

The space $M_{\mu/i,j}$ spanned by all partial derivatives of the lattice polynomial $\Delta_{\mu/i,j}(X;Y)$ is investigated in math.CO/9809126 and many conjectures are given. Here, we prove all these conjectures for the $Y$-free component $M_{\mu/i,j}^0$ of $M_{\mu/i,j}$. In particular, we give an explicit bases for $M_{\mu/i,j}^0$ which allow us to prove directly the central {\sl four term recurrence} for these spaces.

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