Narayana polynomials and Hall-Littlewood symmetric functions

TL;DR

This paper reveals that Narayana polynomials are a specific case of row Hall-Littlewood symmetric functions and extends formulas for Catalan numbers using lambda-ring calculus.

Contribution

It establishes a connection between Narayana polynomials and Hall-Littlewood functions and generalizes Catalan number formulas with lambda-ring calculus.

Findings

Narayana polynomials are a specialization of row Hall-Littlewood functions

Generalization of Catalan number formulas using lambda-ring calculus

Provides new insights into symmetric functions and combinatorial polynomials

Abstract

We show that Narayana polynomials are a specialization of row Hall-Littlewood symmetric functions. Using lambda-ring calculus, we generalize to Narayana polynomials the formulas of Koshy and Jonah for Catalan numbers.