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Vanishing Ideals of Lattice Diagram Determinants

✍ Scribed by J.-C. Aval; N. Bergeron

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
206 KB
Volume
99
Category
Article
ISSN
0097-3165

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✦ Synopsis

A lattice diagram is a finite set L ¼ fðp 1 ; q 1 Þ; . . . ; ðp n ; q n Þg of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is

pj i y qj i jj: The space M L is the space spanned by all partial derivatives of D L ðX n ; Y n Þ: We denote by M 0 L the Y -free component of M L : For m a partition of n þ 1; we denote by m=ij the diagram obtained by removing the cell ði; jÞ from the Ferrers diagram of m: Using homogeneous partially symmetric polynomials, we give here a dual description of the vanishing ideal of the space M 0 m and we give the first known description of the vanishing ideal of M 0 m=ij : # 2002 Elsevier Science (USA)

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