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PreprintarXiv licencearXiv

Strong q-log-convexity of the d-Hoggatt polynomials

  • Shane Chern
  • Wenle Shi
Open at sourcePDFDOICite

Abstract

In this paper, three (q-)log-convexity or concavity properties related to the d-Hoggatt numbers are investigated. First, we show that the d-Hoggatt transformation preserves the log-convexity of a sequence. We then establish the strong q-log-concavity of a q-analog of d-Hoggatt numbers. Finally, we prove the core result of this work, namely, the sequence of d-Hoggatt polynomials is strongly q-log-convex, based on the theory of Schur functions.

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Cite

BibTeXRIS
BibTeX
@misc{chern2026strong,
  title = {{Strong $q$-log-convexity of the $d$-Hoggatt polynomials}},
  author = {Shane Chern and Wenle Shi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33732},
  eprint = {2609.33732},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33732},
}
RIS
TY  - UNPB
TI  - Strong q-log-convexity of the d-Hoggatt polynomials
AU  - Shane Chern
AU  - Wenle Shi
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33732
UR  - https://arxiv.org/abs/2609.33732
AB  - In this paper, three (q-)log-convexity or concavity properties related to the d-Hoggatt numbers are investigated. First, we show that the d-Hoggatt transformation preserves the log-convexity of a sequence. We then establish the strong q-log-concavity of a q-analog of d-Hoggatt numbers. Finally, we prove the core result of this work, namely, the sequence of d-Hoggatt polynomials is strongly q-log-convex, based on the theory of Schur functions.
ER  -