AbstractLet G be a chordal graph and I(G) its edge ideal. Let β(I(G))=(β0,β1,…,βp) denote the Betti sequence of I(G), where βi stands for the ith total Betti number of I(G) and where p is the projective dimension of I(G). It will be shown that there exists a simplicial complex Δ of dimension p whose f-vector f(Δ)=(f0,f1,…,fp) coincides with β(I(G))
Abstract. Let ∆ be a simplicial complex, and ∆s the shifted simplicial complex of ∆, as defined by K...
Thesis (Ph.D.)--University of Washington, 2016-08The f-vector of a simplicial complex is a fundament...
The Betti-numbers of a graded ideal I in a polynomial ring and the Betti-numbers of its generic init...
AbstractLet G be a chordal graph and I(G) its edge ideal. Let β(I(G))=(β0,β1,…,βp) denote the Betti ...
This thesis compiles results in four related areas. • Jump Sequences of Edge Ideals: Given a graph G...
Let A be a (d + 1) \Theta d real matrix whose row vectors positively span R d and which is generic...
We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a n...
Betti numbers are topological invariants that count the number of holes of each dimension in a spac...
In this paper we describe the convex hulls of the sets of f- and β-vectors of different classes of s...
In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard compl...
This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (grap...
Let G be a finite simple graph on n vertices. Let JG⊂K[x1,…,xn] be the cover ideal of G. In this art...
AbstractLet Δn be the simplicial complex of squarefree positive integers less than or equal to n ord...
We give a combinatorial formula for the Betti numbers which appear in a minimal free resolution of ...
Abstract. The emergence of Boij-Söderberg theory has given rise to new connections between combinat...
Abstract. Let ∆ be a simplicial complex, and ∆s the shifted simplicial complex of ∆, as defined by K...
Thesis (Ph.D.)--University of Washington, 2016-08The f-vector of a simplicial complex is a fundament...
The Betti-numbers of a graded ideal I in a polynomial ring and the Betti-numbers of its generic init...
AbstractLet G be a chordal graph and I(G) its edge ideal. Let β(I(G))=(β0,β1,…,βp) denote the Betti ...
This thesis compiles results in four related areas. • Jump Sequences of Edge Ideals: Given a graph G...
Let A be a (d + 1) \Theta d real matrix whose row vectors positively span R d and which is generic...
We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a n...
Betti numbers are topological invariants that count the number of holes of each dimension in a spac...
In this paper we describe the convex hulls of the sets of f- and β-vectors of different classes of s...
In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard compl...
This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (grap...
Let G be a finite simple graph on n vertices. Let JG⊂K[x1,…,xn] be the cover ideal of G. In this art...
AbstractLet Δn be the simplicial complex of squarefree positive integers less than or equal to n ord...
We give a combinatorial formula for the Betti numbers which appear in a minimal free resolution of ...
Abstract. The emergence of Boij-Söderberg theory has given rise to new connections between combinat...
Abstract. Let ∆ be a simplicial complex, and ∆s the shifted simplicial complex of ∆, as defined by K...
Thesis (Ph.D.)--University of Washington, 2016-08The f-vector of a simplicial complex is a fundament...
The Betti-numbers of a graded ideal I in a polynomial ring and the Betti-numbers of its generic init...
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