Journal of Commutative Algebra

Toric representations of algebras defined by certain nonsimple polyominoes

Akihiro Shikama

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Abstract

In this paper, we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.

Article information

Source
J. Commut. Algebra, Volume 10, Number 2 (2018), 265-274.

Dates
First available in Project Euclid: 13 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.jca/1534125828

Digital Object Identifier
doi:10.1216/JCA-2018-10-2-265

Zentralblatt MATH identifier
06917496

Subjects
Primary: 05E40: Combinatorial aspects of commutative algebra 13C05: Structure, classification theorems

Keywords
Polyominoes toric ideals toric rings

Citation

Shikama, Akihiro. Toric representations of algebras defined by certain nonsimple polyominoes. J. Commut. Algebra 10 (2018), no. 2, 265--274. doi:10.1216/JCA-2018-10-2-265. https://projecteuclid.org/euclid.jca/1534125828


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References

  • A. Conca, Ladder determinantal rings, J. Pure Appl. Alg. 98 (1995), 119–134.
  • J. Herzog, A.A. Qureshi and A. Shikama, Gröbner bases of balanced polyominoes, Math. Nachr. 288 (2015), 775–783.
  • J. Herzog and S. Saeedi Madani, The coordinate ring of a simple polyomino, Illinois J. Math. 58 (2014), 981–995.
  • T. Hibi and A.A. Qureshi, Nonsimple polyominoes and prime ideals, Illinois J. Math., to appear.
  • H. Narasimhan, The irreducibility of ladder determinantal varieties, J. Algebra 102 (1986), 171–223.
  • A.A. Qureshi, Ideals generated by $2$-minors, collections of cells and stack polyominoes, J. Algebra 357 (2012), 279–303.
  • A.A. Qureshi, T. Shibuta and A. Shikama, Simple polyominoes are prime, J. Commutative Algebra, to appear.
  • A. Shikama, Toric rings of nonsimple polyominoes, Int. J. Alg. 9 (2015), 195–201.
  • B. Sturmfels, Gröbner bases and convex polytopes, American Mathematical Society, Providence, RI, 1995.