What is dilated pooling and how it works mathematically?
From Tensorflow Github:

Dilated max-pooling is simply regular max-pooling but the pixels/voxels you use in each &quot;application&quot; of the max-pooling operation are exactly the same pixels/voxels you would select with dilated convolution.
Dilated convolution/pooling are useful for connectomics and 3D shape datasets (3D deep learning).

So, similarly as in convolution every nth pixel is selected for the operation.
Edit
Selecting points like this:

making pooling for them like this:

Picture sources:
https://www.quora.com/Is-a-pooling-layer-necessary-in-CNN-Can-it-be-replaced-by-convolution
https://www.quora.com/What-is-max-pooling-in-convolutional-neural-networks
Edit2:
2 x 2 max pooling with 3 x 3 dilation:
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0 (5) 0  0 [6] 0  0 (3) 0  0 [6] 0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0 (3) 0  0 (4) 0  0 (2) 0  0 (4) 0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0 (1  0  0 (2) 0  0 (2) 0  0 (1) 0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0 (3) 0  0 [4] 0  0 [6] 0  0 (3) 0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0
0  0  0  0  0  0  0  0  0  0  0  0  0  0

becomes
6  6
4  6