RADICAL PROPERTY OF POLYOMINO IDEALS
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....
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| Format: | Dissertations |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/79043 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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