Bounded Height Interlaced Pairs of Parking Functions

TL;DR

This paper provides an explicit enumeration formula for interlaced pairs of parking functions with Dyck paths of bounded height, using Chebyshev-like polynomials with symmetric function coefficients.

Contribution

It introduces a novel enumeration formula for bounded height interlaced parking function pairs using advanced polynomial and symmetric function techniques.

Findings

Explicit enumeration formula derived

Utilizes Chebyshev-like polynomials with symmetric coefficients

Advances understanding of parking functions with bounded Dyck path height

Abstract

We enumerate interlaced pairs of parking functions whose underlying Dyck path has a bounded height. We obtain an explicit formula for this enumeration in the form of a quotient of analogs of Chebicheff polynomials having coefficients in the ring of symmetric functions.