Column-reading order of standard Young tableaux
= Column-reading order of standard Young tableaux
Read each column from top to bottom, with columns ordered from left to right, and compare the resulting words lexicographically. With <Young symmetrizer> convention $h_t=c_tr_t$, this order gives <triangular vanishing of Young-symmetrizer products>. Changing the symmetrizer product convention requires a compatible order, rather than retaining a fixed vanishing direction automatically.