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Journal of Commutative Algebra
Article
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arXiv.org e-Print Archive
Preprint . 2015
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Project Euclid
Other literature type . 2017
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Journal of Commutative Algebra
Article . 2017 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2015
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https://dx.doi.org/10.1216/jca...
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Claim

Simple polyominoes are prime

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jun 2017Embargo end date: 01 Jan 2015Publisher:Rocky Mountain Mathematics ConsortiumJournal:Journal of Commutative Algebra, volume 9 (issn: 1939-2346, Copyright policy )
Authors: Qureshi, Ayesha Asloob; Shibuta, Takafumi; Shikama, Akihiro;

doi: 10.1216/jca-2017-9-3-413 , 10.48550/arxiv.1501.05107

arXiv: 1501.05107

Simple polyominoes are prime

Abstract

In this paper we show that polyomino ideal of a simple polyomino coincides with the toric ideal of a weakly chordal bipartite graph and hence it has a quadratic Gr��bner basis with respect to a suitable monomial order.

Keywords

weakly chordal graphs, 13C05, Polyominoes, FOS: Mathematics, 05E40, toric ideals, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 13C05, 05E40, 13P10, Gröbner basis, 13P10

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 14
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
14
Top 10%
Top 10%
Average
Green
bronze