19 citations · 19 across the 5 of their papers we have counts for
9 papers
Degree of -polynomials of edge ideals
Jennifer Biermann, Selvi Kara, Augustine O'Keefe +2
In this paper, we investigate the degree of -polynomials of edge ideals of finite simple graphs. In particular, we provide combinatorial formulas for the degree of the -polyn…
Down-left graphs and a connection to toric ideals of graphs
Jennifer Biermann, Beth Anne Castellano, Marcella Manivel +2
We introduce a family of graphs, which we call down-left graphs, and study their combinatorial and algebraic properties. We show that members of this family are well-covered, …
Toric Ideals of Weighted Oriented Graphs
Jennifer Biermann, Selvi Kara, Kuei-Nuan Lin +1
Given a vertex-weighted oriented graph, we can associate to it a set of monomials. We consider the toric ideal whose defining map is given by these monomials. We find a generating…
Algebraic invariants of weighted oriented graphs
Selvi Kara, Jennifer Biermann, Kuei-Nuan Lin +1
Let be a weighted oriented graph and let be its edge ideal in a polynomial ring . We give the formula of Castelnuovo-Mumford regularity of $R/I(\m…
Betti numbers of symmetric shifted ideals
Jennifer Biermann, Hernán De Alba, Federico Galetto +5
We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the…
Bounds on the regularity of toric ideals of graphs
Jennifer Biermann, Augustine O'Keefe, Adam Van Tuyl
Let be a finite simple graph. We give a lower bound for the Castelnuovo-Mumford regularity of the toric ideal associated to in terms of the sizes and number of induce…
Generalized cover ideals and the persistence property
Ashwini Bhat, Jennifer Biermann, Adam Van Tuyl
Let be a square-free monomial ideal in , and consider the sets of associated primes for all integers . Although it is known th…
Partial coloring, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes
Jennifer Biermann, Christopher A. Francisco, Huy Tài Hà +1
In attempting to understand how combinatorial modifications alter algebraic properties of monomial ideals, several authors have investigated the process of adding "whiskers" to gra…
Balanced vertex decomposable simplicial complexes and their h-vectors
Jennifer Biermann, Adam Van Tuyl
Given any finite simplicial complex Δ, we show how to construct a new simplicial complex Δ_χ that is balanced and vertex decomposable. Moreover, we show that the h-vector of the si…