A recursive formula for the number of semi-Heyting algebras definable on a finite chain

TL;DR

This paper introduces a recursive method to count semi-Heyting algebras on finite chains, providing a new formula and comparison to existing counts, advancing algebraic enumeration techniques.

Contribution

It presents a novel recursive construction for semi-Heyting algebras on chains and derives a new counting formula, improving understanding of their structure.

Findings

Derived a recursive formula for counting semi-Heyting algebras on chains

Compared new counting formula with previously known results

Enhanced enumeration methods for algebraic structures on finite chains

Abstract

We provide a recursive construction of all the semi-Heyting algebras that can be defined on a chain with $n$ elements. This construction allows us to count them easily. We also compare the formula for the number of semi-Heyting chains thus obtained to the one previously known.