Revitalized automatic proofs: demonstrations

TL;DR

This paper generalizes identities related to the Catalan triangle, demonstrates automated proofs with novel twists, and occasionally provides combinatorial proofs, advancing the understanding of these mathematical structures.

Contribution

It introduces generalized identities for the Catalan triangle and showcases automated proof techniques with innovative elements, including combinatorial proofs.

Findings

Generalizations of Catalan triangle identities

Automated proofs with new twists

Occasional combinatorial proofs

Abstract

We consider three problems from the recent issues of the American Mathematical Monthly involving different versions of Catalan triangle. Our main results offer generalizations of these identities and demonstrate automated proofs with additional twists, and on occasion we furnish a combinatorial proof.