Table 1 Rules for prime tangles
From: RNA secondary structure factorization in prime tangles
Rule type | Rule id | Rule | ||||
|---|---|---|---|---|---|---|
Delete | R1 | \(T_i \circ T_i\) | = | \(I_N\) | Â | Â |
R2 | \(U_i \circ U_i\) | = | \(U_i\) | Â | Â | |
R3 | \(T_i \circ U_i\) | = | \(U_i\) | Â | Â | |
R4 | \(U_i \circ T_i\) | = | \(U_i\) | Â | Â | |
R5 | \(U_i \circ U_j \circ U_i\) | = | \(U_i\) | \(\iff\) | \(|i-j| = 1\) | |
R6 | \(U_i \circ T_j \circ U_i\) | = | \(U_i\) | \(\iff\) | \(|i-j| = 1\) | |
R7 | \(T_i \circ U_j \circ U_i\) | = | \(T_j \circ U_i\) | \(\iff\) | \(|i-j| = 1\) | |
R8 | \(U_i \circ U_j \circ T_i\) | = | \(U_i \circ T_j\) | \(\iff\) | \(|i-j| = 1\) | |
R9 | \(U_i \circ T_j \circ T_i\) | = | \(U_i \circ U_j\) | \(\iff\) | \(|i-j| = 1\) | |
R10 | \(T_i \circ T_j \circ U_i\) | = | \(U_j \circ U_i\) | \(\iff\) | \(|i-j| = 1\) | |
Move | R11 | \(T_i \circ T_j \circ T_i\) | = | \(T_j \circ T_i \circ T_j\) | \(\iff\) | \(|i-j| = 1\) |
R12 | \(T_i \circ U_j \circ T_i\) | = | \(T_j \circ U_i \circ T_j\) | \(\iff\) | \(|i-j| = 1\) | |
R13 | \(P_i \circ P_j\) | = | \(P_j \circ P_i\) | \(\iff\) | \(|i-j| > 1\) | |