(untitled) (European Journal of Pure and Applied Mathematics, 2024)
A polyomino is a finite set of unit squares joined side by side on the Cartesian plane. Qureshi introduced an ideal constructed from a polyomino which is called "polyomino ideal". In this paper, we study the binomials arising from Buchberger Algorithm on polyomino ideals. We also introduce socket wrench polyominoes and study the Gröbner bases of the ideal I_P and some algebraic properties of K[P].