30 citations · 184 across the 67 of their papers we have counts for
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Behaviors of pairs of dimensions and depths of edge ideals
Akihiro Higashitani, Akane Kanno, Ryota Ueji
Edge ideals of finite simple graphs on vertices are the ideals of the polynomial ring in variables generated by the quadratic monomials associated with the e…
The -vectors of the edge rings of a special family of graphs
Akihiro Higashitani, Nayana Shibu Deepthi
The -vectors of homogeneous rings are one of the most important invariants that often reflect ring-theoretic properties. On the other hand, there are few examples of edge rings…
Levelness versus almost Gorensteinness of edge rings of complete multipartite graphs
Akihiro Higashitani, Koji Matsushita
Levelness and almost Gorensteinness are well-studied properties on graded rings as a generalized notion of Gorensteinness. In the present paper, we study those properties for the e…
Inequalities of invariants on Stanley-Reisner rings of Cohen-Macaulay simplicial complexes
Akihiro Higashitani, Hiroju Kanno, Kazunori Matsuda
The goal of the present paper is the study of some algebraic invariants of Stanley-Reisner rings of Cohen-Macaulay simplicial complexes of dimension . We prove that the ineq…
Conic divisorial ideals and non-commutative crepant resolutions of edge rings of complete multipartite graphs
Akihiro Higashitani, Koji Matsushita
The first goal of the present paper is to study the class groups of the edge rings of complete multipartite graphs, denoted by , where $1 \leq r_1 \leq \…
Quadratic Gröbner bases of block diagonal matching field ideals and toric degenerations of Grassmannians
Akihiro Higashitani, Hidefumi Ohsugi
In the present paper, we prove that the toric ideals of certain -block diagonal matching fields have quadratic Gröbner bases. Thus, in particular, those are quadratically genera…