An interactive example of a theorem from the upcoming paper "Webification of plane partitions" (2025+), Ashleigh Adams and Jessica Striker.
Instructions: Drag the big web (on the left) to rotate both webs. (This feature currently does not work on phones.)
Description: The SL_4-web on the left is in bijection with the fundamental domain of a totally symmetric self-complementary plane partition. One can map the web on the left to the SL_2-web on the right (Adams, Striker 2025+). Underneath both webs is the lattice word of the web. By rotating the webs, we see how rotaiton on the webs and promotion on the words match.
\[
\mathsf{pro}^k(\omega) \quad \text{as } k \text{ increases, with } \omega = 1112\overline{4}2\overline{4}2(34)44(34)(34)
\]
