Three families of $q$-Lommel polynomials
Combinatorics
2021-11-01 v3 Classical Analysis and ODEs
Abstract
Three -versions of Lommel polynomials are studied. Included are explicit representations, recurrences, continued fractions, and connections to associated Askey--Wilson polynomials. Combinatorial results are emphasized, including a general theorem when moments coincide with orthogonal polynomial moments. The combinatorial results use weighted Motzkin paths, Schr\"oder paths, and parallelogram polyominoes.
Keywords
Cite
@article{arxiv.2105.10096,
title = {Three families of $q$-Lommel polynomials},
author = {Jang Soo Kim and Dennis Stanton},
journal= {arXiv preprint arXiv:2105.10096},
year = {2021}
}
Comments
24 pages, 4 figures