Binomials Arising from Buchberger Algorithm on Polyomino Ideals

Authors

  • Yoshua Hamonangan Bandung Institute of Technology
  • Intan Muchtadi-Alamsyah Bandung Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5016

Keywords:

radical, Ideal, Buchberger Algorithm, Gr\"{o}bner Bases, Polyomino

Abstract

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 Gr\"{o}bner bases of the ideal $I_{\mathcal P}$ and some algebraic properties of $K[\mathcal P]$. 

Author Biographies

  • Yoshua Hamonangan, Bandung Institute of Technology

    Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences,  Bandung Institute of Technology, Bandung, West Java, Indonesia

  • Intan Muchtadi-Alamsyah, Bandung Institute of Technology

    Algebra Research Group, Faculty of Mathematics and Natural Sciences,  Bandung Institute of Technology, Bandung, West Java, Indonesia

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Binomials Arising from Buchberger Algorithm on Polyomino Ideals. (2024). European Journal of Pure and Applied Mathematics, 17(4), 2621-2650. https://doi.org/10.29020/nybg.ejpam.v17i4.5016