Tilings with T-tetrominoes
refreshments at 3:45pm
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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