arXiv subjects

Yuta Hatasa

Publications and source records attributed to Yuta Hatasa.

3 recordsLinked to original sources

arXiv2026

Almost Gorenstein edge rings of bipartite graphs and their $h$-vectors

We characterize bipartite graphs whose edge rings are almost Gorenstein. Using this characterization, we recover known results for two families of graphs. In addition, we show that if the edge ring of a bipartite graph is almost Gorenstein and its $h$-polynomial has degree at least two, then the $h$-polynomial is palindromic except possibly for the linear and next-to-leading coefficients. Moreover, we construct two bipartite graphs whose edge rings have the same $h$-vector, although only one of the rings is almost Gorenstein.

math.AC↗

arXiv2026

A palindromicity criterion for the $h$-polynomials of bipartite edge rings

We study a symmetry problem for the $h$-polynomials of edge rings of bipartite graphs. Let $G$ be a bipartite graph and write $h(\mathbb{k}[G];t)=h_0+h_1t+\cdots+h_st^s$. We prove that if $\Bbbk[G]$ is pseudo-Gorenstein and $h_1=h_{s-1}$, then $\Bbbk[G]$ is Gorenstein. Equivalently, under these assumptions the $h$-polynomial of $\Bbbk[G]$ is palindromic. The proof treats the $2$-connected case first by translating the numerical condition $h_1=h_{s-1}$ into a tight-separation condition for non-edges, and then passes to arbitrary bipartite graphs using the block decomposition. We also construct a blockwise minimal Gorenstein closure, obtained by adjoining all non-edges not separated by tight acceptable sets, and show that this construction preserves the next-to-leading coefficient of the $h$-polynomial.

math.AC↗

arXiv2024

Pseudo-Gorenstein edge rings and a new family of almost Gorenstein edge rings

In this paper, we study edge rings and their $h$-polynomials. We investigate when edge rings are pseudo-Gorenstein, which means that the leading coefficients of the $h$-polynomials of edge rings are equal to $1$. Moreover, we compute the $h$-polynomials of a special family of edge rings and show that some of them are almost Gorenstein.

math.AC↗