Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Shikama, Akihiro"'
It is shown that for large classes of posets $P$ and $Q$, the defining ideal $J_{P,Q}$ of an isotonian algebras is generated by squarefree binomials. Within these classes, those posets are classified for which $J_{P,Q}$ is quadratically generated.
Externí odkaz:
http://arxiv.org/abs/1609.00595
To a pair $P$ and $Q$ of finite posets we attach the toric ring $K[P,Q]$ whose generators are in bijection to the isotone maps from $P$ to $Q$. This class of algebras, called isotonian, are natural generalizations of the so-called Hibi rings. We dete
Externí odkaz:
http://arxiv.org/abs/1512.01973
Autor:
Shikama, Akihiro
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.
Externí odkaz:
http://arxiv.org/abs/1511.04204
In the present paper, we introduce a multibasic extension of the Ehrhart theory. We give a multibasic extension of Ehrhart polynomials and Ehrhart series. We also show that an analogue of Ehrhart reciprocity holds for multibasic Ehrhart polynomials.
Externí odkaz:
http://arxiv.org/abs/1509.03121
Let $P$ be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope ${\mathcal O}(P)$ is equal to that of the chain polytope ${\mathcal C}(P)$. Furthermore, it will be shown that the degree sequence
Externí odkaz:
http://arxiv.org/abs/1508.00187
For a pair $(P,Q)$ of finite posets the generators of the ideal $L(P,Q)$ correspond bijectively to the isotone maps from $P$ to $Q$. In this note we determine all pairs $(P,Q)$ for which the Alexander dual of $L(P,Q)$ coincides with $L(Q,P)$, up to a
Externí odkaz:
http://arxiv.org/abs/1504.01520
Autor:
Shikama, Akihiro
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 polyominoes which are of the form "rectangle minus rectangle".
Externí odkaz:
http://arxiv.org/abs/1503.04782
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\"obner basis with respect to a suitable monomial order.
Externí odkaz:
http://arxiv.org/abs/1501.05107
Edge polytopes is a class of interesting polytope with rich algebraic and combinatorial properties, which was introduced by Ohsugi and Hibi. In this papar, we follow a previous study on cutting edge polytopes by Hibi, Li and Zhang. Instead of focusin
Externí odkaz:
http://arxiv.org/abs/1406.1942
We introduce balanced polyominoes and show that their ideal of inner minors is a prime ideal and has a quadratic Gr\"obner basis with respect to any monomial order, and we show that any row or column convex and any tree-like polyomino is simple and b
Externí odkaz:
http://arxiv.org/abs/1403.6920