Abstract: Polyominoes are two-dimensional figures which are originally rooted in recreational mathematics and combinatorics, and extensively discussed in connection with tiling problems of the plane. The first connection of polyominoes with commutative algebra appeared in [1] by assigning each polyomino the ideal of its inner 2-minors or the polyomino ideal.
In this talk, I will explain the algebraic properties of polyomino ideal purely based on the combinatorics of polyomino.
Reference: [1] A. A. Qureshi, Ideals generated by 2-minors, collections of cells and stack polyominoes, J. Algebra, 357, 279-303, (2012).
