Alladi Ramakrishnan Hall

Algebraic insights into polyominoes via Knutson ideals

Nirmal Kotal

IMSc

Polyominoes are geometric shapes made by connecting equal-sized squares edge to edge, and they have been extensively studied in
combinatorics, particularly in the context of tiling problems. In 2012, Qureshi established a novel connection between polyominoes and
commutative algebra by associating each polyomino with a binomial ideal, referred to as a polyomino ideal. Meanwhile, Knutson ideals are a class of ideals in a polynomial ring, known for their rich algebraic properties, including connections to Grobner bases, radicality, and
Frobenius splitting. In this talk, we will explore how Knutson ideals can be applied to analyze the algebraic properties of polyomino ideals.

This is an ongoing collaborative project with Mitra Koley and Dharm Veer.