... Austria.Submitted: February 20 , 1995; Accepted: July 9, 1995Bijective proofs of the hook formulas for the number of ordinary standardYoung tableaux and for the number of shifted standard Young tableaux ... latter subset of ¯X 2 by¯OR. Observe that the sign of w(Y,∅, 0,U) for all quadruples in¯ORis sgn(0)=1,which is positive. Clearly, the set OR of right-hand side objects of (4 .2) is ... Frame, Robinson and Thrall’s [1] hook formula for the number of standard Young tableaux of a given shape. This resulted in the discovery of threedifferent such proofs [2, 10, 14], none of them is...