The sharp height-three cutoff for P-partition uniqueness
Year: 2026
Type: preprint
Abstract: For naturally labeled posets of Greene shape (3,2,2,1^k), the P-partition generating function distinguishes all orders up to isomorphism exactly when k is at most four. At k=4 an exhaustive enumeration using a four-element marked core gives 143,069 isomorphism classes, separated by three exact specializations. Common padding by isolated vertices transfers the lower bound to smaller k. A twelve-element pair gives equality at k=5. The cutoff is presented as a candidate theorem.
Author: Barritz, Robert
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225643283