Proof of Cigler's conjecture on q-Hoggatt numbers
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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