Séminaire Lotharingien de Combinatoire, 87B.8 (2023), 25 pp.

Jang Soo Kim and Dennis Stanton

Three families of q-Lommel polynomials

Abstract. Three q-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 RI moments coincide with orthogonal polynomial moments. The combinatorial results use weighted Motzkin paths, Schröder paths, and parallelogram polyominoes.

Received: July 26, 2022. Revised: July 24, 2023. Published: August 31, 2023.

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If you need to cite this article, here is a bibtex:

@article{KimStanton23,
author = {Kim, Jang Soo and Stanton, Dennis},
title = {{Three families of $q$-Lommel polynomials}},
fjournal = {S{\'e}minaire Lotharingien de Combinatoire},
journal = {S{\'e}min. Lothar. Combin.},
issn={1286-4889},
volume = {87B},
number= {8},
pages = {1--25},
year = {2023},
language = {English},
doi={10.48550/arXiv.2105.10096},
}