# Higher analogs of simplicial and combinatorial complexity

## TL;DR

This paper introduces higher analogs of simplicial and combinatorial complexity, establishing relationships with existing topological and combinatorial invariants to deepen understanding of complex structures.

## Contribution

It defines higher simplicial and combinatorial complexities and connects them to topological and combinatorial invariants, expanding the theoretical framework.

## Key findings

- Higher simplicial complexity relates to higher topological complexity.
- Higher combinatorial complexity connects with the simplicial complexity of order complexes.
- The paper establishes new theoretical relationships between these complexities.

## Abstract

We introduce higher simplicial complexity of a simplicial complex $K$ and higher combinatorial complexity of a finite space $P$ (i.e. $P$ is a finite poset). We relate higher simplicial complexity with higher topological complexity of $|K|$ and higher combinatorial complexity with higher simplicial complexity of the order complex of $P$.