Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chern, Shane, Shi, Wenle
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214725787