Combinatorial Variations on Cantor's Diagonal

TL;DR

This paper explores finite versions of Cantor's diagonal, introduces refined counting methods, and establishes connections between Cantorian tableaux and hypergraph colorings, advancing combinatorial enumeration and structural understanding.

Contribution

It refines an equivalence relation for counting finite Cantorian tableaux and links these structures to hypergraph colorings, providing new enumerative results.

Findings

Refined enumeration of finite Cantorian tableaux.

Established correspondence between Cantorian tableaux and hypergraph colorings.

Extended previous counting results with new equivalence relations.

Abstract

We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative results follow and allow to look at the sub-class of the so- called bi-Cantorian tableaux. We conclude with a correspondence between Cantorian-type tableaux and coloring of hypergraphs having a square number of vertices.