ASSOCIATION OF MULTIPLE ZETA-VALUE WITH POSITIVE KNOTS VIA FEYNMAN DIAGRAMS UP TO 9 LOOPS

It is found that the number, Mn, of irreducible multiple zeta values ( MZVs) of weight n, is generated by 1x(2)-x(3)=Pi(n)(1-x(n))(Mn). For 9 greater than or equal to n greater than or equal to 3, M(n) enumerate s positive knots with n crossings. Positive knots to which field theor y assigns knot-numbers that are not MZVs first appear at 10 crossings. We identify all the positive knots, up to 15 crossings, that are in c orrespondence with irreducible MZVs, by virtue of the connection betwe en knots and numbers realized by Feynman diagrams with up to 9 loops.