Tilings with T-tetrominoes

Mike Korn

MIT

November 5,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

A T-tetromino is the figure formed by attaching four unit squares together in the shape of a T. In this talk we consider the problem of tiling a region with T-tetrominoes. We show that for a particular class of regions, the number of T-tetromino tilings is an evaluation of the Tutte polynomial of a graph related to the region. Furthermore, using a height-function approach, we show that the set of all T-tetromino tilings of such a region forms a distributive lattice, and that any two tilings of such a region are connected by local moves. Along the way we observe connections to the square-ice model of statistical mechanics, domino tilings, and alternating-sign matrices. Joint work with Igor Pak.


Speaker's Contact Info: mikekorn(at-sign)math.mit.edu


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