Manuscript En05-C@1 · En05-C.tex · section · aa213ea6

Algebraic backward recursion

Stage F: ancestry, matched replacements, and metric bounds › Algebraic backward recursion · lines 1451–1462

En05-C@1#eq:backwardsets

For terminal region $Y$ and terminal tick $T$ , define

N_{T} (Y) = Y, N_{s} (Y) = U_{s} (N_{s + 1} (Y)) .

Let

T_{s : T} = T_{s} \circ T_{s + 1} \circ \dots \circ T_{T - 1} .

Displayed formulas in this passage

En05-C@1#eq:backwardsets · line 1454
$N_{T} (Y) = Y, N_{s} (Y) = U_{s} (N_{s + 1} (Y)) .$
unlabeled · line 1459
$T_{s : T} = T_{s} \circ T_{s + 1} \circ \dots \circ T_{T - 1} .$