# Total positivity of Narayana matrices

## TL;DR

This paper proves the total positivity of Narayana matrices of types A and B, confirming previous conjectures and establishing strict total positivity for their squares, advancing understanding in combinatorial matrix theory.

## Contribution

It establishes the total positivity and strict total positivity of Narayana matrices and squares of types A and B, confirming longstanding conjectures.

## Key findings

- Proved total positivity of Narayana matrices of types A and B.
- Confirmed conjectures of Chen, Liang, Wang, Pan, and Zeng.
- Established strict total positivity of Narayana squares of types A and B.

## Abstract

We prove the total positivity of the Narayana triangles of type $A$ and type $B$, and thus affirmatively confirm a conjecture of Chen, Liang and Wang and a conjecture of Pan and Zeng. We also prove the strict total positivity of the Narayana squares of type $A$ and type $B$.