72 citations · 97 across the 7 of their papers we have counts for
12 papers
Chordality, syzygies, and shellability for hypergraphic analogues of interval graphs
Anton Dochtermann, Bennet Goeckner, Marta Pavelka
Interval graphs are a special class of chordal graphs, and hence have connections to commutative algebra via Fröberg's theorem that characterizes linear resolutions of squarefree q…
Vertex orders in higher dimensions
Bennet Goeckner, Marta Pavelka
Unit interval and interval complexes are higher-dimensional generalizations of unit interval and interval graphs, respectively. We show that strongly connected unit interval comple…
The Existence and Structure of Universal Partial Cycles
Dylan Fillmore, Bennet Goeckner, Rachel Kirsch +2
A universal partial cycle (or upcycle) for is a cyclic sequence that covers each word of length over the alphabet exactly once -- like a De Bruijn…
A characterization of two-dimensional Buchsbaum matching complexes
Bennet Goeckner, Fran Herr, Legrand Jones +1
The matching complex of a graph is the set of all matchings in . A Buchsbaum simplicial complex is a generalization of both a homology manifold and a Cohen--Macaulay…
Minkowski summands of cubes
Federico Castillo, Joseph Doolittle, Bennet Goeckner +2
In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit comput…
Lattice polytopes from Schur and symmetric Grothendieck polynomials
Margaret Bayer, Bennet Goeckner, Su Ji Hong +5
Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope i…
Partition and Cohen-Macaulay Extenders
Joseph Doolittle, Bennet Goeckner, Alexander Lazar
If a pure simplicial complex is partitionable, then its -vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex…
Manifold Matching Complexes
Margaret Bayer, Bennet Goeckner, Marija Jelić Milutinović
The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper we complete…
Resolving Stanley's conjecture on -fold acyclic complexes
Joseph Doolittle, Bennet Goeckner
In 1993 Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank boolean intervals whose minimal faces t…
Higher Nerves of Simplicial Complexes
Hailong Dao, Joseph Doolittle, Ken Duna +3
We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of t…
Universal Partial Words over Non-Binary Alphabets
Bennet Goeckner, Corbin Groothuis, Cyrus Hettle +4
Chen, Kitaev, Mütze, and Sun recently introduced the notion of universal partial words, a generalization of universal words and de Bruijn sequences. Universal partial words allow f…
A non-partitionable Cohen-Macaulay simplicial complex
Art M. Duval, Bennet Goeckner, Caroline J. Klivans +1
A long-standing conjecture of Stanley states that every Cohen-Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. D…