8 citations · 9 across the 8 of their papers we have counts for
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Geometrically vertex decomposable star configurations
Susan M. Cooper, Emanuela Marangone, Elena Guardo +1
The goal of this paper is to determine how the family of ideals of star configurations intersects with the class of geometrically vertex decomposable ideals. The main result of thi…
The van der Waerden Simplicial Complex and its Lefschetz Properties
Naveena Ragunathan, Adam Van Tuyl
The van der Waerden simplicial complex, denoted , is the simpicial complex whose facets correspond to the arithmetic progressions of length in the set $\{1,\ldo…
Comparing the -number and -polynomials of edge ideals
Kamalesh Saha, Adam Van Tuyl
In this paper, we compare the -numbers and the degree of the -polynomials associated with edge ideals of connected graphs. We prove that the -number can…
Partial Betti splittings with applications to binomial edge ideals
A. V. Jayanthan, Aniketh Sivakumar, Adam Van Tuyl
We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, Hà, and Van Tuyl. Given a homoge…
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…