In Search of Hyperpaths

Amir Dahari*, Nathan Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Hypertrees are high-dimensional counterparts of graph theoretic trees. They have attracted a great deal of attention by various investigators. Here we introduce and study hyperpaths—a particular class of hypertrees which are high dimensional analogs of paths in graph theory. A d-dimensional hyperpath is a d-dimensional hypertree in which every (d- 1) -dimensional face is contained in at most (d+ 1) faces of dimension d. We introduce a possibly infinite family of hyperpaths for every dimension, and investigate its properties in greater depth for dimension d= 2.

Original languageAmerican English
Pages (from-to)399-421
Number of pages23
JournalDiscrete and Computational Geometry
Volume69
Issue number2
DOIs
StatePublished - Mar 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Finite fields
  • High dimensional combinatorics
  • Hypertrees
  • Linear algebra
  • Matrix multiplication
  • Simplicial complexes

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