ScalingStacks

Definition 3.6. The type of a web $W$ in any of the complexes in (3.1) is the element $\tau(W)\in\{p,t\}^{M}$ that records in the $j$-th coordinate whether the $j$-th internal crossing in the respective link diagram is resolved in a parallel way (p), or using the thick edge (t).

The offset of a web $W$ in any of the complexes $\left\llbracket L^{i}_{\pm}\right\rrbracket$ is the element $o(W)\in\{p,t\}$ that records the resolution of the leftmost external crossing.

The state of a web $W$ in any of the complexes $\left\llbracket L^{i}_{\pm}\right\rrbracket$ for $1\leq i\leq x-1$ is the element $s(W)\in\{p,t\}^{2n}$, which records the resolutions of the $2n$ rightmost external crossings (that is, all except the leftmost external crossing). Such a web $W$ is said to be palindromic if $s(W)$ is a palindrome.