6 papers
Comparisons between ordinary and symbolic powers of edge ideals with respect to regularity and depth
Yuji Muta
In this paper, we investigate the difference between ordinary and symbolic powers of edge ideals on the Castelnuovo-Mumford regularity and the depth. As a main theorem, we prove th…
Symbolic Rees algebras of complementary edge ideals
Antonino Ficarra, Somayeh Moradi, Yuji Muta
Let be a finite simple graph on and let denote its complementary edge ideal in the polynomial ring . We give a combinatorial description, i…
Algebraic study on rooted products of graphs and multi-clique corona graphs
Yuji Muta, Naoki Terai
In this paper, we study rooted products of graphs from the perspective of combinatorial commutative algebra. For edge ideals, we introduce the 2-Cohen-Macaulayness with respect to…
The Serre depth of Stanley-Reisner rings and the depth of their symbolic powers
Yuji Muta, Naoki Terai
We investigate an invariant, called the Serre depth, from the perspective of combinatorial commutative algebra. In this paper, we establish several properties of an analogue of the…
On minimal free resolutions of the cover ideals of clique-whiskered graphs
Yuji Muta, Naoki Terai
We explicitly construct a minimal free resolution of the cover ideals of clique-whiskered graphs. In particular, Cohen--Macaulay chordal graphs, clique corona graphs, and Cohen--Ma…
The v-numbers of Stanley-Reisner ideals from the viewpoint of Alexander dual complexes
Tatsuya Kataoka, Yuji Muta, Naoki Terai
We express the v-number of the Stanley-Reisner ideal in terms of its Alexander dual complex and prove that the v-number of a cover ideal is just two less than the initial degree of…