English

Three families of $q$-Lommel polynomials

Combinatorics 2021-11-01 v3 Classical Analysis and ODEs

Abstract

Three qq-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 RIR_I 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