40 citations · 95 across the 43 of their papers we have counts for
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Three invariants of geometrically vertex decomposable ideals
Thai Thanh Nguyen, Jenna Rajchgot, Adam Van Tuyl
We study three invariants of geometrically vertex decomposable ideals: the Castelnuovo-Mumford regularity, the multiplicity, and the -invariant. We show that these invariants ca…
Conditions for Virtually Cohen--Macaulay Simplicial Complexes
Jay Yang, Adam Van Tuyl
A simplicial complex is a virtually Cohen-Macaulay simplicial complex if its associated Stanley-Reisner ring has a virtual resolution, as defined by Berkesch, Erman, and Sm…
Fröberg's Theorem, vertex splittability and higher independence complexes
Priyavrat Deshpande, Amit Roy, Anurag Singh +1
A celebrated theorem of Fröberg gives a complete combinatorial classification of quadratic square-free monomial ideals with a linear resolution. A generalization of this theorem to…
The weak Lefschetz property of whiskered graphs
Susan M. Cooper, Sara Faridi, Thiago Holleben +2
We consider Artinian level algebras arising from the whiskering of a graph. Employing a result by Dao-Nair we show that multiplication by a general linear form has maximal rank in…
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, …
Comparing invariants of toric ideals of bipartite graphs
Kieran Bhaskara, Adam Van Tuyl
Let be a finite simple graph and let denote its associated toric ideal in the polynomial ring . For each integer , we completely determine all the possible va…
Condition Numbers of Hessenberg Companion Matrices
Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl +1
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion ma…