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           18:00 - 20:00     Commutative Algebra Webinar
Algebraic Aspects of Polyominoes

School
MATHEMATICS

Polyominoes are, roughly speaking, plane figures obtained by joining squares of equal size (cells) edge to edge. We establish a connection of polyominoes to commutative algebra by assigning to each polyomino its ideal of inner minors (also called Polyomino ideals). This class of ideals widely generalizes the ideal of 2-minors of a matrix of indeterminates, and even the ideal of 2-minors of twosided ladders. It also includes the meet-join ideal of planar distributive lattices. Typically one determines for such ideals their Grobner bases, determines their resolution and computes their regularity, checks whether the rings defined by them ...