# Multi-tribrackets

## TL;DR

This paper introduces multi-tribrackets, a new algebraic framework for coloring knot and link diagrams with different operations at various crossings, enhancing the ability to distinguish complex links.

## Contribution

It develops the concept of multi-tribrackets, including component multi-tribrackets, and demonstrates their effectiveness in distinguishing links beyond standard tribracket invariants.

## Key findings

- Multi-tribrackets can distinguish links not separable by standard tribracket invariants.
- Examples show the effectiveness of multi-tribracket counting invariants.
- Reinterpretation of previous results in terms of multi-tribrackets.

## Abstract

We introduce multi-tribrackets, algebraic structures for region coloring of diagrams of knots and links with different operations at different kinds of crossings. In particular we consider the case of component multi-tribrackets which have different tribracket operations at single-component crossings and multi-component crossings. We provide examples to show that the resulting counting invariants can distinguish links which are not distinguished by the counting invariants associated to the standard tribracket coloring. We reinterpret the results of [11] in terms of multi-tribrackets and consider futuredirections for multi-tribracket theory.