# Skew Schur Function Representation of Directed Paths in a Slit

## TL;DR

This paper links the enumeration of weighted directed paths with skew Schur functions, generalizing previous work that connected excursions to rectangular Schur functions, thus broadening the combinatorial understanding of path enumeration.

## Contribution

It introduces a general relationship between weighted directed path enumeration and skew Schur functions, extending prior results on excursions and rectangular Schur functions.

## Key findings

- Established a connection between path enumeration and skew Schur functions
- Extended Bousquet-Mélou's work from rectangular to skew Schur functions
- Provided a new combinatorial framework for analyzing directed paths

## Abstract

In this work, we establish a general relationship between the enumeration of weighted directed paths and skew Schur functions, extending work by Bousquet-M\'elou, who expressed generating functions of discrete excursions in terms of rectangular Schur functions.