Journal of Combinatorics

Volume 12 (2021)

Number 4

Skew Schur function representation of directed paths in a slit

Pages: 571 – 588

DOI: https://dx.doi.org/10.4310/JOC.2021.v12.n4.a3

Authors

Anum Khalid (School of Mathematical Sciences, Queen Mary University of London, United Kingdom)

Thomas Prellberg (School of Mathematical Sciences, Queen Mary University of London, United Kingdom)

Abstract

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

Keywords

Schur functions, directed paths

2010 Mathematics Subject Classification

Primary 05Axx, 05Exx. Secondary 05A15, 05E05, 05E10.

Received 15 October 2019

Accepted 27 September 2020

Published 31 January 2022