q-Whittaker Domino Shuffling     domino-tilings

Forward EKLP Shuffling builds random tilings of Aztec diamonds via the map A_n → A_n+1:

1. Delete bad blocks: Remove colliding pairs: N-S (N bottom, S top) and E-W (E left, W right)
2. Slide: Each domino slides one unit in its direction (N↑, S↓, E→, W←)
3. Fill holes: Fill each empty 2×2 block with a random domino pair

Enable "Granular steps" to see each phase separately. Bad blocks are highlighted in red before deletion.

q-Whittaker Deformation (TODO)

The q-Whittaker deformation of domino shuffling modifies Step 3 (Fill holes) to introduce correlations between adjacent empty blocks based on partition-valued stopping probabilities.

For a working implementation using the partition-based q-Whittaker algorithm (via RSK growth diagrams), see:

• q-RSK Sampling of Domino Tilings — samples from q-Whittaker measure using growth diagram dynamics

The challenge for direct shuffling is translating partition indices (where islands are detected as consecutive i with μ_i − κ_i = 1) into geometric empty-block positions.

References:

• arXiv:math/9201305 — Elkies, Kuperberg, Larsen, Propp (EKLP shuffling)
• arXiv:1504.00666 — Matveev, Petrov (q-RSK and q-Whittaker)