The Standard Polynomial As An Identity On Symplectic Matrices

We choose a particular basis where each basis element can be represented on a graph of 2n points by a pair of labelled, directed edges. A pseudo-Eulerian path on this graph is defined as a path in which exactly one edge of each pair of edges is traversed exactly once. By counting the number of pseudo-Eulerian paths and assigning a value of $-$1 or +1 to each, the value of $S\sb{k}$ can be determined. (Abstract shortened by UMI.).