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Lattice Diagram polynomials in one set of variables

Abstract

The space Mμ/i,jM_{\mu/i,j} spanned by all partial derivatives of the lattice polynomial Δμ/i,j(X;Y)\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 YY-free component Mμ/i,j0M_{\mu/i,j}^0 of Mμ/i,jM_{\mu/i,j}. In particular, we give an explicit bases for Mμ/i,j0M_{\mu/i,j}^0 which allow us to prove directly the central {\sl four term recurrence} for these spaces.Comment: 15 page

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