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.
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- Finite fields
- High dimensional combinatorics
- Linear algebra
- Matrix multiplication
- Simplicial complexes