Small Rotation Blocks and the Order-Six Stable Marriage Problem
Year: 2026
Type: preprint
Abstract: We prove that a finite poset with at most fifteen elements, width at most three, and the following common-incomparability property has at most 48 antichains: for every x < y, the elements incomparable with both x and y form a chain of size at most two. An explicit fifteen-element poset attains the bound. We show that order-six stable-marriage rotation posets satisfy these hypotheses by examining convex rotation blocks and their fixed partner pools. This gives a structural upper bound of 48 stable matchings, matching the lower bound already provided by Benjamin, Converse, and Krieger in 1995. Equality forces fifteen rotations, all of size two, and every one of the 36 man–woman pairs occurs in some stable matching. Provenance note: This preprint is accompanied by reproducible verification artifacts and a partial Lean formalization. The Lean development verifies the finite-poset core and supporting components; it does not formalize the entire stable-marriage theorem f(6) = 48 end to end. The source-code and reproducibility repository is available at https://github.com/insammael/stable-marriage-f6 and is linked as a related resource. Version v09 adds the public Palomar record for the finite-poset theorem (Theorem 4.8), registered as PALOMAR-2026-09-20-000010, version 1: https://palomar-registry.org/entry?id=PALOMAR-2026-09-20-000010&version=1. The registered declaration passed Comparator checks and replay by both the Lean kernel and the independent NanoDa kernel. The Palomar record concerns the finite-poset theorem only, not an end-to-end formalization of the full stable-marriage theorem f(6)=48. The mathematical content of the preprint is unchanged from v08.
Author: Jo, Myunglae
Institution: Kyungpook National University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213764291
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