5 citations · 17 across the 13 of their papers we have counts for
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Toric representations of algebras defined by certain nonsimple polyominoes
Akihiro Shikama
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.
Isotonian Algebras
Mina Bigdeli, Jürgen Herzog, Takayuki Hibi +2
To a pair and of finite posets we attach the toric ring whose generators are in bijection to the isotone maps from to . This class of algebras, called isoto…
Alexander duality for monomial ideals associated with isotone maps between posets
Juergen Herzog, Ayesha Asloob Qureshi, Akihiro Shikama
For a pair of finite posets the generators of the ideal correspond bijectively to the isotone maps from to . In this note we determine all pairs for…
Toric rings of nonsimple polyominoes
Akihiro Shikama
It is known that toric ring of a simple polyomino is ring homomorphic to a edge ring of a weakly chordal bipartite graph. In this paper we identify the toric ring of nonsimple poly…
Simple Polyominoes are Prime
Ayesha Asloob Qureshi, Takafumi Shibuta, Akihiro Shikama
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 Gröbner basis with…