2014/09/23 by Karim Adiprasito, Karim A. Adiprasito, Afshin Goodarzi +4 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.AC #math.CO
paper · pdf · doi:10.48550/arxiv.1409.6657
4 pages, minor changes
openalex publication_date 2014/09/23 · arxiv created 2014/11/11 · arxiv updated 2014/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis and Bjorner. In this note, we provide a unifying approach which allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley--Reisner rings.