Threshold complexes and connections to number theory

Pakianathan, Jonathan; Winfree, Troy

doi:10.3906/mat-1112-14

Turkish Journal of Mathematics

2013

DOI: 10.3906/mat-1112-14

|View full text |Cite

Threshold complexes and connections to number theory

Jonathan Pakianathan¹,

Troy Winfree²

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2020

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 16 publications

(21 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Minkowski complexes and convex threshold dimension

Frick

Sanyal

2017

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

For a collection of convex bodies P1, . . . , Pn ⊂ R d containing the origin, a Minkowski complex is given by those subsets whose Minkowski sum does not contain a fixed basepoint. Every simplicial complex can be realized as a Minkowski complex and for convex bodies on the real line, this recovers the class of threshold complexes. The purpose of this note is the study of the convex threshold dimension of a complex, that is, the smallest dimension in which it can be realized as a Minkowski complex. In particular, we show that the convex threshold dimension can be arbitrarily large. This is related to work of Chvátal and Hammer (1977) regarding forbidden subgraphs of threshold graphs. We also show that convexity is crucial this context.

show abstract

Minkowski complexes and convex threshold dimension

Frick

Sanyal

2017

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

show abstract

Fundamental properties of Björner's complexes

Noguchi

2020

Topology and its Applications

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Threshold complexes and connections to number theory

Cited by 2 publications

References 16 publications

Minkowski complexes and convex threshold dimension

Minkowski complexes and convex threshold dimension

Fundamental properties of Björner's complexes

Contact Info

Product

Resources

About