3 papers
math.CO2026
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…
math.CO2025
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…
math.CO2024
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…