Rank-3 scale theorems: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
Tags: Mobile edit Mobile web edit |
||
| Line 87: | Line 87: | ||
* v_3 = A_3 X + B_3 Q. | * v_3 = A_3 X + B_3 Q. | ||
If some A_i and A_j differed by more than 2, a contradiction would result, as all intermediate combinations must be attained (since scooting over by one step changes the numbers of Q's and X's by <= 1). So we assume | If some A_i and A_j differed by more than 2, a contradiction would result, as all intermediate combinations must be attained (since scooting over by one step changes the numbers of Q's and X's by <= 1). So we assume we have sizes | ||
* v_1 = AX + BQ, | * v_1 = AX + BQ, | ||
* v_2 = (A-1)X + (B+1)Q, | * v_2 = (A-1)X + (B+1)Q, | ||