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arXiv · 2609.33732

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

Shane Chern·Wenle Shi
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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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Shane Chern, Wenle Shi. 2026-09-27. Strong $q$-log-convexity of the $d$-Hoggatt polynomials. https://arxiv.org/abs/2609.33732

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