We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs. In particular, we draw heavily from the topic of dominating sets. Through Hochster’s Formula, we recover and strengthen existing results on the homological connectivity of graph independence complexes.

Let G be a simple graph on n vertices and JG denote the binomial edge ideal of in polynomial ring S=K[x1,…,xn,y1,…,yn]. In this article, we compute second graded Betti numbers JG, obtain minimal presentation it when is tree or unicyclic graph. We classify all graphs whose ideals are almost complete intersection, prove that they generated by d-sequence Rees algebra their Cohen-Macaulay. also an ...

In this paper, we provide some exact formulas for the projective dimension and regularity of powers edge ideals vertex-weighted rooted forests. These are functions weight vertices number edges.

In 1992, Thomas Bier introduced a surprisingly simply way to construct a large number of simplicial spheres. He proved that, for any simplicial complex ∆ on the vertex set V with ∆ 6= 2 , the deleted join of ∆ with its Alexander dual ∆∨ is a combinatorial sphere. In this paper, we extend Bier’s construction to multicomplexes, and study their combinatorial and algebraic properties. We show that ...

Experiments are performed on a 82.5 sweep flat-plate delta wing combined with a dorsal fin of height 0.6 of the wing semi-span at Reynolds number based on the wing root chord of 3.32×105, in which a pair of small and short dielectric barrier discharge plasma actuators are employed at the wing leading edge near the apex of the wing to effect flow control. Measured pressure distributions over the...