Lattice Diagram polynomials in one set of variables

Abstract

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.

15 pages

References in corpus (1)

• Vanishing ideals of Lattice Diagram determinants

Cited by in corpus (3)

• Vanishing ideals of Lattice Diagram determinants
• (GL_k x S_n)-modules and nabla of hook-indexed Schur functions
• On certain spaces of lattice diagram polynomials