A note on the minors of a symmetric matrix

We give a concise representation for the minors of an arbitrary symmetric matrix with entries in any ring or field. More exactly, each summand of the specified determinant is given in terms of so-called spanning forests, i.~e.\ minimal spanning connected subgraphs, of the complete graph on $n+1$ vertices, $n$ the size of the matrix. This generalizes a formula for special minors and $n=3$ given by {\sc Conway} and {\sc Sloane}.

Preprint, January 2000.   (dvi-file, 7KB)