[dynamic_sausage]

This text seems to quickly get rather technical, with theorems and stuff. I would suggest looking at Golomb's classical Polyominoes first https://archive.org/details/polyominoes00golo/page/n7/mode/2...

If you like playing with polyominoes, there is a really fun chesslike table game inspired by them called Blokus, and someone wrote an open-source engine for it: https://pentobi.sourceforge.io/

Of course, as already noted in another comment, there's the ultimate tetromino game: Tetris (literally defined as tetromino tennis)...

[cableshaft]

There's tons of polyomino games that have come out in the past 8 or so years. I wouldn't necessarily say they do a better job than Blokus did (imo, I really like Blokus), but it's interesting to see what game designers have been doing with the concept lately.

Uwe Rosenberg in particular has designed a bunch of games playing around with the polyomino concept, starting with Patchwork, then a trilogy of games Indian Summer, Cottage Garden, and Spring Meadow, and then culminating in a rules-heavy game A Feast for Odin.

Phil Walker-Harding designed a very popular one called Barenpark, where you cover spots on a board which unlock different types of tiles and new boards.

A recently released game that's been well received that utilizes a lazy susan for tile selection is called Planet Unknown.

There's also a tile drafting game called Isle of Cats that's quite popular as well.

A game that combines polyominoes with roll and write games that's quite popular is Cartographers.

Patchwork kicked off this new trend in board games, and was released in 2014.