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arXiv · 2606.26950

Proof of Cigler's conjecture on $q$-Hoggatt numbers

Shane Chern·Wenle Shi
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Abstract

We prove the nonnegativity and palindromicity of a family of polynomials arising from $q$-Hoggatt numbers. The nonnegativity is derived from Stanley's $(P,ω)$-partition theory through a standard Young tableau formula, while the palindromicity is proved by an involution on rectangular standard Young tableaux. Our result confirms a conjecture of Cigler.

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Shane Chern, Wenle Shi. 2026-06-25. Proof of Cigler's conjecture on $q$-Hoggatt numbers. https://arxiv.org/abs/2606.26950

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