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)
2002 iii To my wife, Jennifer Wagner, the point in my variety.
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)