RADICAL PROPERTY OF POLYOMINO IDEALS

• Main Author: Yonatan Hamonangan, Yoshua
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/79043
• Institution: Institut Teknologi Bandung

Polyomino is a two dimensional object which originated in combinatorics and recreational mathematics. Relation between polyomino and commutative algebra was first introduced by Qureshi. Qureshi defined the polyomino ideal which is a generalization from the class of 2-minor ideal of m × n matrix. There are some results about the prime polyomino ideal from previous researchers. Not all polyominoes have a prime polyomino ideal but later the ideals are known to be a radical ideal. Since every prime ideal is a radical ideal, Qureshi conjectures that every polyomino ideal is a radical ideal. To investigate the conjecture, a reasearch about the generators of the initial ideal from polyomino ideal was done. One of the generators of the initial ideal is the Gr¨obner basis which can be obtained from the Buchberger Algorithm. This dissertation examines how the Buchberger Algorithm is performed on polyomino ideals. At the end of this dissertation, a class of polyominoes that are not prime but radical were given.