Year: 2026
Type: preprint
Abstract: Let X and Y be finite ordered sets and let $X^Y$ denote the ordered set of order-preserving maps from $Y$ to $X$. Let $t$ be a~term formed from a~single variable by exponentiation. We prove that, for every term $t$ with at most twelve variable occurrences and arbitrary finite ordered sets $A,B$, $t(A)\cong t(B)$ implies that $A\cong B$. General constructions and reconstruction principles are developed first; the second part gives the occurrence-by-occurrence proofs. At twelve occurrences the proof covers 4,766 interchange normal forms, representing all 58,786 binary parenthesizations, including 40 exceptional forms. Two additional unbounded reconstruction families, complete finite audit data, and 457 exact height-comparison certificates are included.
Source: arXiv (Cornell University)
Author: Grätzer, George
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220740494