Proofs Of Three Geode Conjectures
Tewodros Amdeberhan, Doron Zeilberger
TL;DR
This paper proves three conjectures about Geode numbers, a new class of multi-indexed numbers introduced from Hyper-Catalan numbers, advancing understanding in this mathematical area.
Contribution
It provides formal proofs for three conjectures related to Geode numbers, a novel mathematical construct derived from Hyper-Catalan numbers.
Findings
Proof of three conjectures about Geode numbers
Establishment of foundational properties of Geode numbers
Advancement in the theory of multi-indexed number systems
Abstract
In the May 2025 issue of the Amer. Math. Monthly, Norman J. Wildberger and Dean Rubine intoduced a new kind of multi-indexed numbers, that they call `Geode numbers', obtained from the Hyper-Catalan numbers. They posed three intriguing conjectures about them, that are proved in this note.
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