Adriano Garsia

Mark Haiman2
Nolan R Wallach2
Co-Chair Chair1
2Mark Haiman
2Nolan R Wallach
1Co-Chair Chair
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We obtain explicit formulas for the enumeration of labelled parallelogram polyominoes. These are the polyominoes that are bounded, above and below, by northeast lattice paths going from the origin to a point (k, n). The numbers from 1 to n (the labels) are bijectively attached to the n north steps of the above-bounding path, with the condition that they(More)
Let p 1 p n 0, and p = detkx p j i k n i;j=1. Let Mp be the linear span of the partial derivatives of p. Then Mp is a graded Sn-module. We prove that it is the direct sum of graded left regular representations of Sn. Speciically, set j = p j , n , j, and let t be the Hilbert polynomial of the span of all skew Schur functions s = as varies in. Then the(More)
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