Some observations about Hankel determinants of the columns of Pascal triangle and related topics

TL;DR

This paper explores properties and conjectures related to Hankel determinants of Pascal triangle columns, connecting them to combinatorial objects like Young tableaux and Narayana numbers, revealing intriguing mathematical relationships.

Contribution

It compiles facts and conjectures about Hankel determinants of Hoggatt triangle columns, highlighting their connections to combinatorial structures.

Findings

Identifies relationships between Hankel determinants and Young tableaux.

Proposes conjectures linking Hankel determinants to Narayana numbers.

Provides a collection of known facts and open questions.

Abstract

This note collects some facts and conjectures about the Hankel determinants and their generating functions of the columns of Hoggatt triangles which apparently are related to combinatorial objects such as Young tableaux and Narayana numbers.