In Search of Hyperpaths

Amir Dahari; Nathan Linial

doi:10.1007/s00454-021-00360-x

In Search of Hyperpaths

Amir Dahari^*, Nathan Linial

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English
Pages (from-to)	399-421
Number of pages	23
Journal	Discrete and Computational Geometry
Volume	69
Issue number	2
DOIs	https://doi.org/10.1007/s00454-021-00360-x
State	Published - 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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10.1007/s00454-021-00360-x

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AB - 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.

KW - Finite fields

KW - High dimensional combinatorics

KW - Hypertrees

KW - Linear algebra

KW - Matrix multiplication

KW - Simplicial complexes

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ER -

In Search of Hyperpaths

Abstract

Bibliographical note

Keywords

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